diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet index c449d9d..efb09f8 100644 --- a/books/bookvol10.2.pamphlet +++ b/books/bookvol10.2.pamphlet @@ -380,6 +380,40 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{ArcHyperbolicFunctionCategory}{AHYP} \pagepic{ps/v102archyperbolicfunctioncategory.ps}{AHYP}{1.00} +<>= +)set break resume +)sys rm -f ArcHyperbolicFunctionCategory.output +)spool ArcHyperbolicFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ArcHyperbolicFunctionCategory +--R ArcHyperbolicFunctionCategory is a category constructor +--R Abbreviation for ArcHyperbolicFunctionCategory is AHYP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for AHYP +--R +--R------------------------------- Operations -------------------------------- +--R acosh : % -> % acoth : % -> % +--R acsch : % -> % asech : % -> % +--R asinh : % -> % atanh : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ArcHyperbolicFunctionCategory examples +==================================================================== + +See Also: +o )show ArcHyperbolicFunctionCategory + +@ {\bf See:} @@ -457,6 +491,40 @@ digraph pic { The {\tt asec} and {\tt acsc} functions were modified to include an intermediate test to check that the argument has a reciprocal values. +<>= +)set break resume +)sys rm -f ArcTrigonometricFunctionCategory.output +)spool ArcTrigonometricFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ArcTrigonometricFunctionCategory +--R ArcTrigonometricFunctionCategory is a category constructor +--R Abbreviation for ArcTrigonometricFunctionCategory is ATRIG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATRIG +--R +--R------------------------------- Operations -------------------------------- +--R acos : % -> % acot : % -> % +--R acsc : % -> % asec : % -> % +--R asin : % -> % atan : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ArcTrigonometricFunctionCategory examples +==================================================================== + +See Also: +o )show ArcTrigonometricFunctionCategory + +@ {\bf See:} \pageto{TranscendentalFunctionCategory}{TRANFUN} @@ -712,6 +780,38 @@ digraph pic { \pagehead{BasicType}{BASTYPE} \pagepic{ps/v102basictype.ps}{BASTYPE}{1.00} +<>= +)set break resume +)sys rm -f BasicType.output +)spool BasicType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BasicType +--R BasicType is a category constructor +--R Abbreviation for BasicType is BASTYPE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BASTYPE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BasicType examples +==================================================================== + +See Also: +o )show BasicType + +@ {\bf See:} \pageto{BlowUpMethodCategory}{BLMETCT} @@ -787,6 +887,38 @@ digraph pic { \pagehead{CoercibleTo}{KOERCE} \pagepic{ps/v102koerce.ps}{KOERCE}{1.00} +<>= +)set break resume +)sys rm -f CoercibleTo.output +)spool CoercibleTo.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CoercibleTo +--R CoercibleTo S: Type is a category constructor +--R Abbreviation for CoercibleTo is KOERCE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for KOERCE +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> S +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CoercibleTo examples +==================================================================== + +See Also: +o )show CoercibleTo + +@ {\bf See:} \pageto{BlowUpMethodCategory}{BLMETCT} @@ -861,6 +993,39 @@ digraph pic { \pagehead{CombinatorialFunctionCategory}{CFCAT} \pagepic{ps/v102combinatorialfunctioncategory.ps}{CFCAT}{1.00} +<>= +)set break resume +)sys rm -f CombinatorialFunctionCategory.output +)spool CombinatorialFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CombinatorialFunctionCategory +--R CombinatorialFunctionCategory is a category constructor +--R Abbreviation for CombinatorialFunctionCategory is CFCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CFCAT +--R +--R------------------------------- Operations -------------------------------- +--R binomial : (%,%) -> % factorial : % -> % +--R permutation : (%,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CombinatorialFunctionCategory examples +==================================================================== + +See Also: +o )show CombinatorialFunctionCategory + +@ {\bf See:} \pageto{CombinatorialOpsCategory}{COMBOPC} @@ -937,6 +1102,38 @@ digraph pic { \pagehead{ConvertibleTo}{KONVERT} \pagepic{ps/v102konvert.ps}{KONVERT}{1.00} +<>= +)set break resume +)sys rm -f ConvertibleTo.output +)spool ConvertibleTo.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ConvertibleTo +--R ConvertibleTo S: Type is a category constructor +--R Abbreviation for ConvertibleTo is KONVERT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for KONVERT +--R +--R------------------------------- Operations -------------------------------- +--R convert : % -> S +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ConvertibleTo examples +==================================================================== + +See Also: +o )show ConvertibleTo + +@ {\bf See:} \pageto{Collection}{CLAGG} @@ -1063,6 +1260,39 @@ digraph pic { \pagehead{ElementaryFunctionCategory}{ELEMFUN} \pagepic{ps/v102elementaryfunctioncategory.ps}{ELEMFUN}{1.00} +<>= +)set break resume +)sys rm -f ElementaryFunctionCategory.output +)spool ElementaryFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ElementaryFunctionCategory +--R ElementaryFunctionCategory is a category constructor +--R Abbreviation for ElementaryFunctionCategory is ELEMFUN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ELEMFUN +--R +--R------------------------------- Operations -------------------------------- +--R ?**? : (%,%) -> % exp : % -> % +--R log : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ElementaryFunctionCategory examples +==================================================================== + +See Also: +o )show ElementaryFunctionCategory + +@ {\bf See:} \pageto{TranscendentalFunctionCategory}{TRANFUN} @@ -1134,6 +1364,38 @@ digraph pic { \pagehead{Eltable}{ELTAB} \pagepic{ps/v102eltab.ps}{ELTAB}{1.00} +<>= +)set break resume +)sys rm -f Eltable.output +)spool Eltable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Eltable +--R Eltable(S: SetCategory,Index: Type) is a category constructor +--R Abbreviation for Eltable is ELTAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ELTAB +--R +--R------------------------------- Operations -------------------------------- +--R ?.? : (%,S) -> Index +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Eltable examples +==================================================================== + +See Also: +o )show Eltable + +@ {\bf See:} \pageto{EltableAggregate}{ELTAGG}\hfill @@ -1222,6 +1484,40 @@ digraph pic { The {\tt csch} and {\tt sech} functions were modified to include an intermediate test to check that the argument has a reciprocal values. +<>= +)set break resume +)sys rm -f HyperbolicFunctionCategory.output +)spool HyperbolicFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show HyperbolicFunctionCategory +--R HyperbolicFunctionCategory is a category constructor +--R Abbreviation for HyperbolicFunctionCategory is HYPCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for HYPCAT +--R +--R------------------------------- Operations -------------------------------- +--R cosh : % -> % coth : % -> % +--R csch : % -> % sech : % -> % +--R sinh : % -> % tanh : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +HyperbolicFunctionCategory examples +==================================================================== + +See Also: +o )show HyperbolicFunctionCategory + +@ {\bf See:} \pageto{TranscendentalFunctionCategory}{TRANFUN} @@ -1312,6 +1608,38 @@ digraph pic { \pagehead{InnerEvalable}{IEVALAB} \pagepic{ps/v102innerevalable.ps}{IEVALAB}{1.00} +<>= +)set break resume +)sys rm -f InnerEvalable.output +)spool InnerEvalable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerEvalable +--R InnerEvalable(A: SetCategory,B: Type) is a category constructor +--R Abbreviation for InnerEvalable is IEVALAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for IEVALAB +--R +--R------------------------------- Operations -------------------------------- +--R eval : (%,A,B) -> % eval : (%,List A,List B) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerEvalable examples +==================================================================== + +See Also: +o )show InnerEvalable + +@ {\bf See:} \pageto{DesingTreeCategory}{DSTRCAT} @@ -1421,6 +1749,40 @@ digraph pic { \pagehead{OpenMath}{OM} \pagepic{ps/v102openmath.ps}{OM}{1.00} +<>= +)set break resume +)sys rm -f OpenMath.output +)spool OpenMath.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OpenMath +--R OpenMath is a category constructor +--R Abbreviation for OpenMath is OM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OM +--R +--R------------------------------- Operations -------------------------------- +--R OMwrite : % -> String OMwrite : (%,Boolean) -> String +--R OMwrite : (OpenMathDevice,%) -> Void +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OpenMath examples +==================================================================== + +See Also: +o )show OpenMath + +@ {\bf See:} \pageto{StringCategory}{STRICAT} @@ -1499,6 +1861,54 @@ digraph pic { \pagehead{PartialTranscendentalFunctions}{PTRANFN} \pagepic{ps/v102partialtranscendentalfunctions.ps}{PTRANFN}{1.00} +<>= +)set break resume +)sys rm -f PartialTranscendentalFunctions.output +)spool PartialTranscendentalFunctions.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PartialTranscendentalFunctions +--R PartialTranscendentalFunctions K: TranscendentalFunctionCategory is a category constructor +--R Abbreviation for PartialTranscendentalFunctions is PTRANFN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PTRANFN +--R +--R------------------------------- Operations -------------------------------- +--R acosIfCan : K -> Union(K,"failed") acotIfCan : K -> Union(K,"failed") +--R acscIfCan : K -> Union(K,"failed") asecIfCan : K -> Union(K,"failed") +--R asinIfCan : K -> Union(K,"failed") atanIfCan : K -> Union(K,"failed") +--R cosIfCan : K -> Union(K,"failed") coshIfCan : K -> Union(K,"failed") +--R cotIfCan : K -> Union(K,"failed") cothIfCan : K -> Union(K,"failed") +--R cscIfCan : K -> Union(K,"failed") cschIfCan : K -> Union(K,"failed") +--R expIfCan : K -> Union(K,"failed") logIfCan : K -> Union(K,"failed") +--R secIfCan : K -> Union(K,"failed") sechIfCan : K -> Union(K,"failed") +--R sinIfCan : K -> Union(K,"failed") sinhIfCan : K -> Union(K,"failed") +--R tanIfCan : K -> Union(K,"failed") tanhIfCan : K -> Union(K,"failed") +--R acoshIfCan : K -> Union(K,"failed") +--R acothIfCan : K -> Union(K,"failed") +--R acschIfCan : K -> Union(K,"failed") +--R asechIfCan : K -> Union(K,"failed") +--R asinhIfCan : K -> Union(K,"failed") +--R atanhIfCan : K -> Union(K,"failed") +--R nthRootIfCan : (K,NonNegativeInteger) -> Union(K,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PartialTranscendentalFunctions examples +==================================================================== + +See Also: +o )show PartialTranscendentalFunctions + +@ {\bf See:} \pagefrom{Category}{CATEGORY} @@ -1690,6 +2100,39 @@ digraph pic { \pagehead{Patternable}{PATAB} \pagepic{ps/v102patternable.ps}{PATAB}{1.00} +<>= +)set break resume +)sys rm -f Patternable.output +)spool Patternable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Patternable +--R Patternable R: Type is a category constructor +--R Abbreviation for Patternable is PATAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PATAB +--R +--R------------------------------- Operations -------------------------------- +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Patternable examples +==================================================================== + +See Also: +o )show Patternable + +@ {\bf See:} \pageto{ComplexCategory}{COMPCAT} @@ -1774,6 +2217,39 @@ digraph pic { \pagehead{PrimitiveFunctionCategory}{PRIMCAT} \pagepic{ps/v102primitivefunctioncategory.ps}{PRIMCAT}{1.00} +<>= +)set break resume +)sys rm -f PrimitiveFunctionCategory.output +)spool PrimitiveFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PrimitiveFunctionCategory +--R PrimitiveFunctionCategory is a category constructor +--R Abbreviation for PrimitiveFunctionCategory is PRIMCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PRIMCAT +--R +--R------------------------------- Operations -------------------------------- +--R integral : (%,Symbol) -> % +--R integral : (%,SegmentBinding %) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PrimitiveFunctionCategory examples +==================================================================== + +See Also: +o )show PrimitiveFunctionCategory + +@ {\bf See:} \pageto{LiouvillianFunctionCategory}{LFCAT} @@ -1837,6 +2313,39 @@ digraph pic { \pagehead{RadicalCategory}{RADCAT} \pagepic{ps/v102radicalcategory.ps}{RADCAT}{1.00} +<>= +)set break resume +)sys rm -f RadicalCategory.output +)spool RadicalCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RadicalCategory +--R RadicalCategory is a category constructor +--R Abbreviation for RadicalCategory is RADCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RADCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?**? : (%,Fraction Integer) -> % nthRoot : (%,Integer) -> % +--R sqrt : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RadicalCategory examples +==================================================================== + +See Also: +o )show RadicalCategory + +@ {\bf See:} \pageto{AlgebraicallyClosedField}{ACF} @@ -1919,6 +2428,39 @@ digraph pic { \pagehead{RetractableTo}{RETRACT} \pagepic{ps/v102retractableto.ps}{RETRACT}{1.00} +<>= +)set break resume +)sys rm -f RetractableTo.output +)spool RetractableTo.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RetractableTo +--R RetractableTo S: Type is a category constructor +--R Abbreviation for RetractableTo is RETRACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RETRACT +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> % retract : % -> S +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RetractableTo examples +==================================================================== + +See Also: +o )show RetractableTo + +@ {\bf See:} \pageto{DifferentialPolynomialCategory}{DPOLCAT} @@ -2069,6 +2611,43 @@ digraph pic { \pagehead{SpecialFunctionCategory}{SPFCAT} \pagepic{ps/v102specialfunctioncategory.ps}{SPFCAT}{1.00} +<>= +)set break resume +)sys rm -f SpecialFunctionCategory.output +)spool SpecialFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SpecialFunctionCategory +--R SpecialFunctionCategory is a category constructor +--R Abbreviation for SpecialFunctionCategory is SPFCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SPFCAT +--R +--R------------------------------- Operations -------------------------------- +--R Beta : (%,%) -> % Gamma : % -> % +--R Gamma : (%,%) -> % abs : % -> % +--R airyAi : % -> % airyBi : % -> % +--R besselI : (%,%) -> % besselJ : (%,%) -> % +--R besselK : (%,%) -> % besselY : (%,%) -> % +--R digamma : % -> % polygamma : (%,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SpecialFunctionCategory examples +==================================================================== + +See Also: +o )show SpecialFunctionCategory + +@ {\bf See:} \pagefrom{Category}{CATEGORY} @@ -2175,6 +2754,40 @@ digraph pic { The {\tt csc} and {\tt sec} functions were modified to include an intermediate test to check that the argument has a reciprocal values. +<>= +)set break resume +)sys rm -f TrigonometricFunctionCategory.output +)spool TrigonometricFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TrigonometricFunctionCategory +--R TrigonometricFunctionCategory is a category constructor +--R Abbreviation for TrigonometricFunctionCategory is TRIGCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for TRIGCAT +--R +--R------------------------------- Operations -------------------------------- +--R cos : % -> % cot : % -> % +--R csc : % -> % sec : % -> % +--R sin : % -> % tan : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TrigonometricFunctionCategory examples +==================================================================== + +See Also: +o )show TrigonometricFunctionCategory + +@ {\bf See:} \pageto{TranscendentalFunctionCategory}{TRANFUN} @@ -2315,6 +2928,44 @@ digraph pic { \pagehead{Aggregate}{AGG} \pagepic{ps/v102agg.ps}{AGG}{1.00} +<>= +)set break resume +)sys rm -f Aggregate.output +)spool Aggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Aggregate +--R Aggregate is a category constructor +--R Abbreviation for Aggregate is AGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for AGG +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R less? : (%,NonNegativeInteger) -> Boolean +--R more? : (%,NonNegativeInteger) -> Boolean +--R size? : (%,NonNegativeInteger) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Aggregate examples +==================================================================== + +See Also: +o )show Aggregate + +@ {\bf See:} \pageto{HomogeneousAggregate}{HOAGG} @@ -2437,6 +3088,43 @@ digraph pic { \pagehead{CombinatorialOpsCategory}{COMBOPC} \pagepic{ps/v102combinatorialopscategory.ps}{COMBOPC}{1.00} +<>= +)set break resume +)sys rm -f CombinatorialOpsCategory.output +)spool CombinatorialOpsCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CombinatorialOpsCategory +--R CombinatorialOpsCategory is a category constructor +--R Abbreviation for CombinatorialOpsCategory is COMBOPC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for COMBOPC +--R +--R------------------------------- Operations -------------------------------- +--R binomial : (%,%) -> % factorial : % -> % +--R factorials : (%,Symbol) -> % factorials : % -> % +--R permutation : (%,%) -> % product : (%,Symbol) -> % +--R summation : (%,Symbol) -> % +--R product : (%,SegmentBinding %) -> % +--R summation : (%,SegmentBinding %) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CombinatorialOpsCategory examples +==================================================================== + +See Also: +o )show CombinatorialOpsCategory + +@ {\bf See:} \pagefrom{CombinatorialFunctionCategory}{CFCAT} @@ -2533,6 +3221,41 @@ digraph pic { \pagehead{EltableAggregate}{ELTAGG} \pagepic{ps/v102eltableaggregate.ps}{ELTAGG}{0.75} +<>= +)set break resume +)sys rm -f EltableAggregate.output +)spool EltableAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show EltableAggregate +--R EltableAggregate(Dom: SetCategory,Im: Type) is a category constructor +--R Abbreviation for EltableAggregate is ELTAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ELTAGG +--R +--R------------------------------- Operations -------------------------------- +--R elt : (%,Dom,Im) -> Im ?.? : (%,Dom) -> Im +--R qelt : (%,Dom) -> Im +--R qsetelt! : (%,Dom,Im) -> Im if $ has shallowlyMutable +--R setelt : (%,Dom,Im) -> Im if $ has shallowlyMutable +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +EltableAggregate examples +==================================================================== + +See Also: +o )show EltableAggregate + +@ {\bf See:} \pageto{IndexedAggregate}{IXAGG} @@ -2656,6 +3379,39 @@ digraph pic { \pagehead{Evalable}{EVALAB} \pagepic{ps/v102evalable.ps}{EVALAB}{1.00} +<>= +)set break resume +)sys rm -f Evalable.output +)spool Evalable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Evalable +--R Evalable R: SetCategory is a category constructor +--R Abbreviation for Evalable is EVALAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for EVALAB +--R +--R------------------------------- Operations -------------------------------- +--R eval : (%,List Equation R) -> % eval : (%,Equation R) -> % +--R eval : (%,R,R) -> % eval : (%,List R,List R) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Evalable examples +==================================================================== + +See Also: +o )show Evalable + +@ {\bf See:} \pageto{ExpressionSpace}{ES} @@ -2762,6 +3518,38 @@ digraph pic { \pagehead{FortranProgramCategory}{FORTCAT} \pagepic{ps/v102fortranprogramcategory.ps}{FORTCAT}{1.00} +<>= +)set break resume +)sys rm -f FortranProgramCategory.output +)spool FortranProgramCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranProgramCategory +--R FortranProgramCategory is a category constructor +--R Abbreviation for FortranProgramCategory is FORTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FORTCAT +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranProgramCategory examples +==================================================================== + +See Also: +o )show FortranProgramCategory + +@ {\bf See:} \pageto{FortranFunctionCategory}{FORTFN} @@ -2856,6 +3644,45 @@ digraph pic { \pagehead{FullyRetractableTo}{FRETRCT} \pagepic{ps/v102fullyretractableto.ps}{FRETRCT}{1.00} +<>= +)set break resume +)sys rm -f FullyRetractableTo.output +)spool FullyRetractableTo.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FullyRetractableTo +--R FullyRetractableTo S: Type is a category constructor +--R Abbreviation for FullyRetractableTo is FRETRCT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FRETRCT +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> % retract : % -> S +--R coerce : Integer -> % if S has RETRACT INT +--R coerce : Fraction Integer -> % if S has RETRACT FRAC INT +--R retract : % -> Integer if S has RETRACT INT +--R retract : % -> Fraction Integer if S has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FullyRetractableTo examples +==================================================================== + +See Also: +o )show FullyRetractableTo + +@ {\bf See:} \pageto{ComplexCategory}{COMPCAT} @@ -2984,6 +3811,44 @@ digraph pic { \pagehead{FullyPatternMatchable}{FPATMAB} \pagepic{ps/v102fullypatternmatchable.ps}{FPATMAB}{1.00} +<>= +)set break resume +)sys rm -f FullyPatternMatchable.output +)spool FullyPatternMatchable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FullyPatternMatchable +--R FullyPatternMatchable R: Type is a category constructor +--R Abbreviation for FullyPatternMatchable is FPATMAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FPATMAB +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean if R has PATMAB INT or R has PATMAB FLOAT +--R coerce : % -> OutputForm if R has PATMAB INT or R has PATMAB FLOAT +--R hash : % -> SingleInteger if R has PATMAB INT or R has PATMAB FLOAT +--R latex : % -> String if R has PATMAB INT or R has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT +--R ?~=? : (%,%) -> Boolean if R has PATMAB INT or R has PATMAB FLOAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FullyPatternMatchable examples +==================================================================== + +See Also: +o )show FullyPatternMatchable + +@ {\bf See:} \pageto{ComplexCategory}{COMPCAT} @@ -3104,6 +3969,40 @@ digraph pic { \pagehead{Logic}{LOGIC} \pagepic{ps/v102logic.ps}{LOGIC}{1.00} +<>= +)set break resume +)sys rm -f Logic.output +)spool Logic.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Logic +--R Logic is a category constructor +--R Abbreviation for Logic is LOGIC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LOGIC +--R +--R------------------------------- Operations -------------------------------- +--R ?/\? : (%,%) -> % ?=? : (%,%) -> Boolean +--R ?\/? : (%,%) -> % ~? : % -> % +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Logic examples +==================================================================== + +See Also: +o )show Logic + +@ {\bf See:} \pageto{BitAggregate}{BTAGG} @@ -3190,6 +4089,40 @@ digraph pic { \pagehead{PlottablePlaneCurveCategory}{PPCURVE} \pagepic{ps/v102plottableplanecurvecategory.ps}{PPCURVE}{1.00} +<>= +)set break resume +)sys rm -f PlottablePlaneCurveCategory.output +)spool PlottablePlaneCurveCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PlottablePlaneCurveCategory +--R PlottablePlaneCurveCategory is a category constructor +--R Abbreviation for PlottablePlaneCurveCategory is PPCURVE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PPCURVE +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm xRange : % -> Segment DoubleFloat +--R yRange : % -> Segment DoubleFloat +--R listBranches : % -> List List Point DoubleFloat +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PlottablePlaneCurveCategory examples +==================================================================== + +See Also: +o )show PlottablePlaneCurveCategory + +@ {\bf See:} \pagefrom{CoercibleTo}{KOERCE} @@ -3287,6 +4220,40 @@ digraph pic { \pagehead{PlottableSpaceCurveCategory}{PSCURVE} \pagepic{ps/v102plottablespacecurvecategory.ps}{PSCURVE}{1.00} +<>= +)set break resume +)sys rm -f PlottableSpaceCurveCategory.output +)spool PlottableSpaceCurveCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PlottableSpaceCurveCategory +--R PlottableSpaceCurveCategory is a category constructor +--R Abbreviation for PlottableSpaceCurveCategory is PSCURVE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PSCURVE +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm xRange : % -> Segment DoubleFloat +--R yRange : % -> Segment DoubleFloat zRange : % -> Segment DoubleFloat +--R listBranches : % -> List List Point DoubleFloat +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PlottableSpaceCurveCategory examples +==================================================================== + +See Also: +o )show PlottableSpaceCurveCategory + +@ {\bf See:} \pagefrom{CoercibleTo}{KOERCE} @@ -3389,6 +4356,38 @@ digraph pic { \pagehead{RealConstant}{REAL} \pagepic{ps/v102realconstant.ps}{REAL}{1.00} +<>= +)set break resume +)sys rm -f RealConstant.output +)spool RealConstant.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RealConstant +--R RealConstant is a category constructor +--R Abbreviation for RealConstant is REAL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for REAL +--R +--R------------------------------- Operations -------------------------------- +--R convert : % -> Float convert : % -> DoubleFloat +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RealConstant examples +==================================================================== + +See Also: +o )show RealConstant + +@ {\bf See:} \pageto{IntegerNumberSystem}{INS} @@ -3470,6 +4469,42 @@ digraph pic { \pagehead{SegmentCategory}{SEGCAT} \pagepic{ps/v102segmentcategory.ps}{SEGCAT}{1.00} +<>= +)set break resume +)sys rm -f SegmentCategory.output +)spool SegmentCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SegmentCategory +--R SegmentCategory S: Type is a category constructor +--R Abbreviation for SegmentCategory is SEGCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SEGCAT +--R +--R------------------------------- Operations -------------------------------- +--R BY : (%,Integer) -> % ?..? : (S,S) -> % +--R convert : S -> % hi : % -> S +--R high : % -> S incr : % -> Integer +--R lo : % -> S low : % -> S +--R segment : (S,S) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SegmentCategory examples +==================================================================== + +See Also: +o )show SegmentCategory + +@ {\bf See:} \pageto{SegmentExpansionCategory}{SEGXCAT} @@ -3588,6 +4623,40 @@ digraph pic { \pagehead{SetCategory}{SETCAT} \pagepic{ps/v102setcategory.ps}{SETCAT}{1.00} +<>= +)set break resume +)sys rm -f SetCategory.output +)spool SetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SetCategory +--R SetCategory is a category constructor +--R Abbreviation for SetCategory is SETCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SETCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SetCategory examples +==================================================================== + +See Also: +o )show SetCategory + +@ {\bf See:} \pageto{AbelianSemiGroup}{ABELSG} @@ -3714,6 +4783,51 @@ digraph pic { \pagehead{TranscendentalFunctionCategory}{TRANFUN} \pagepic{ps/v102transcendentalfunctioncategory.ps}{TRANFUN}{0.75} +<>= +)set break resume +)sys rm -f TranscendentalFunctionCategory.output +)spool TranscendentalFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TranscendentalFunctionCategory +--R TranscendentalFunctionCategory is a category constructor +--R Abbreviation for TranscendentalFunctionCategory is TRANFUN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for TRANFUN +--R +--R------------------------------- Operations -------------------------------- +--R ?**? : (%,%) -> % acos : % -> % +--R acosh : % -> % acot : % -> % +--R acoth : % -> % acsc : % -> % +--R acsch : % -> % asec : % -> % +--R asech : % -> % asin : % -> % +--R asinh : % -> % atan : % -> % +--R atanh : % -> % cos : % -> % +--R cosh : % -> % cot : % -> % +--R coth : % -> % csc : % -> % +--R csch : % -> % exp : % -> % +--R log : % -> % pi : () -> % +--R sec : % -> % sech : % -> % +--R sin : % -> % sinh : % -> % +--R tan : % -> % tanh : % -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TranscendentalFunctionCategory examples +==================================================================== + +See Also: +o )show TranscendentalFunctionCategory + +@ The {\tt acsch}, {\tt asech}, and {\tt acoth} functions were modified to include an intermediate test to check that the argument has a reciprocal values. @@ -3918,6 +5032,41 @@ digraph pic { \pagehead{AbelianSemiGroup}{ABELSG} \pagepic{ps/v102abeliansemigroup.ps}{ABELSG}{0.75} +<>= +)set break resume +)sys rm -f AbelianSemiGroup.output +)spool AbelianSemiGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AbelianSemiGroup +--R AbelianSemiGroup is a category constructor +--R Abbreviation for AbelianSemiGroup is ABELSG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ABELSG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AbelianSemiGroup examples +==================================================================== + +See Also: +o )show AbelianSemiGroup + +@ {\bf See:} \pageto{AbelianMonoid}{ABELMON} @@ -4425,6 +5574,50 @@ digraph pic { \pagehead{FortranFunctionCategory}{FORTFN} \pagepic{ps/v102fortranfunctioncategory.ps}{FORTFN}{1.00} +<>= +)set break resume +)sys rm -f FortranFunctionCategory.output +)spool FortranFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranFunctionCategory +--R FortranFunctionCategory is a category constructor +--R Abbreviation for FortranFunctionCategory is FORTFN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FORTFN +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R retract : Polynomial Integer -> % retract : Polynomial Float -> % +--R retract : Expression Integer -> % retract : Expression Float -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Fraction Polynomial Integer -> % +--R retract : Fraction Polynomial Float -> % +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Polynomial Float -> Union(%,"failed") +--R retractIfCan : Expression Integer -> Union(%,"failed") +--R retractIfCan : Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranFunctionCategory examples +==================================================================== + +See Also: +o )show FortranFunctionCategory + +@ {\bf See:} \pagefrom{FortranProgramCategory}{FORTCAT} @@ -4572,6 +5765,41 @@ digraph pic { \pagehead{FortranMatrixCategory}{FMC} \pagepic{ps/v102fortranmatrixcategory.ps}{FMC}{1.00} +<>= +)set break resume +)sys rm -f FortranMatrixCategory.output +)spool FortranMatrixCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranMatrixCategory +--R FortranMatrixCategory is a category constructor +--R Abbreviation for FortranMatrixCategory is FMC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FMC +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranMatrixCategory examples +==================================================================== + +See Also: +o )show FortranMatrixCategory + +@ {\bf See:} \pagefrom{FortranProgramCategory}{FORTCAT} @@ -4671,6 +5899,52 @@ digraph pic { \pagehead{FortranMatrixFunctionCategory}{FMFUN} \pagepic{ps/v102fortranmatrixfunctioncategory.ps}{FMFUN}{1.00} +<>= +)set break resume +)sys rm -f FortranMatrixFunctionCategory.output +)spool FortranMatrixFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranMatrixFunctionCategory +--R FortranMatrixFunctionCategory is a category constructor +--R Abbreviation for FortranMatrixFunctionCategory is FMFUN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FMFUN +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Matrix Fraction Polynomial Integer -> % +--R retract : Matrix Fraction Polynomial Float -> % +--R retract : Matrix Polynomial Integer -> % +--R retract : Matrix Polynomial Float -> % +--R retract : Matrix Expression Integer -> % +--R retract : Matrix Expression Float -> % +--R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Expression Integer -> Union(%,"failed") +--R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranMatrixFunctionCategory examples +==================================================================== + +See Also: +o )show FortranMatrixFunctionCategory + +@ {\bf See:} \pagefrom{FortranProgramCategory}{FORTCAT} @@ -4819,6 +6093,41 @@ digraph pic { \pagehead{FortranVectorCategory}{FVC} \pagepic{ps/v102fortranvectorcategory.ps}{FVC}{1.00} +<>= +)set break resume +)sys rm -f FortranVectorCategory.output +)spool FortranVectorCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranVectorCategory +--R FortranVectorCategory is a category constructor +--R Abbreviation for FortranVectorCategory is FVC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FVC +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Vector MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranVectorCategory examples +==================================================================== + +See Also: +o )show FortranVectorCategory + +@ {\bf See:} \pagefrom{FortranProgramCategory}{FORTCAT} @@ -4916,6 +6225,52 @@ digraph pic { \pagehead{FortranVectorFunctionCategory}{FVFUN} \pagepic{ps/v102fortranvectorfunctioncategory.ps}{FVFUN}{1.00} +<>= +)set break resume +)sys rm -f FortranVectorFunctionCategory.output +)spool FortranVectorFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranVectorFunctionCategory +--R FortranVectorFunctionCategory is a category constructor +--R Abbreviation for FortranVectorFunctionCategory is FVFUN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FVFUN +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranVectorFunctionCategory examples +==================================================================== + +See Also: +o )show FortranVectorFunctionCategory + +@ {\bf See:} \pagefrom{FortranProgramCategory}{FORTCAT} @@ -5063,6 +6418,45 @@ digraph pic { \pagehead{FullyEvalableOver}{FEVALAB} \pagepic{ps/v102fullyevalableover.ps}{FEVALAB}{0.75} +<>= +)set break resume +)sys rm -f FullyEvalableOver.output +)spool FullyEvalableOver.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FullyEvalableOver +--R FullyEvalableOver R: SetCategory is a category constructor +--R Abbreviation for FullyEvalableOver is FEVALAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FEVALAB +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> R),%) -> % +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R eval : (%,List R,List R) -> % if R has EVALAB R +--R eval : (%,R,R) -> % if R has EVALAB R +--R eval : (%,Equation R) -> % if R has EVALAB R +--R eval : (%,List Equation R) -> % if R has EVALAB R +--R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FullyEvalableOver examples +==================================================================== + +See Also: +o )show FullyEvalableOver + +@ {\bf See:} \pageto{ComplexCategory}{COMPCAT} @@ -5201,6 +6595,44 @@ digraph pic { \pagehead{FileCategory}{FILECAT} \pagepic{ps/v102filecategory.ps}{FILECAT}{1.00} +<>= +)set break resume +)sys rm -f FileCategory.output +)spool FileCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FileCategory +--R FileCategory(Name: SetCategory,S: SetCategory) is a category constructor +--R Abbreviation for FileCategory is FILECAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FILECAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close! : % -> % +--R coerce : % -> OutputForm flush : % -> Void +--R hash : % -> SingleInteger iomode : % -> String +--R latex : % -> String name : % -> Name +--R open : (Name,String) -> % open : Name -> % +--R read! : % -> S reopen! : (%,String) -> % +--R write! : (%,S) -> S ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FileCategory examples +==================================================================== + +See Also: +o )show FileCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -5346,6 +6778,42 @@ digraph pic { \pagehead{Finite}{FINITE} \pagepic{ps/v102finite.ps}{FINITE}{1.00} +<>= +)set break resume +)sys rm -f Finite.output +)spool Finite.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Finite +--R Finite is a category constructor +--R Abbreviation for Finite is FINITE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FINITE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger index : PositiveInteger -> % +--R latex : % -> String lookup : % -> PositiveInteger +--R random : () -> % size : () -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Finite examples +==================================================================== + +See Also: +o )show Finite + +@ {\bf See:} \pageto{DirectProductCategory}{DIRPCAT} @@ -5464,6 +6932,45 @@ digraph pic { \pagehead{FileNameCategory}{FNCAT} \pagepic{ps/v102filenamecategory.ps}{FNCAT}{0.70} +<>= +)set break resume +)sys rm -f FileNameCategory.output +)spool FileNameCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FileNameCategory +--R FileNameCategory is a category constructor +--R Abbreviation for FileNameCategory is FNCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FNCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> String +--R coerce : String -> % coerce : % -> OutputForm +--R directory : % -> String exists? : % -> Boolean +--R extension : % -> String hash : % -> SingleInteger +--R latex : % -> String name : % -> String +--R new : (String,String,String) -> % readable? : % -> Boolean +--R writable? : % -> Boolean ?~=? : (%,%) -> Boolean +--R filename : (String,String,String) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FileNameCategory examples +==================================================================== + +See Also: +o )show FileNameCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -5603,6 +7110,43 @@ digraph pic { \pagehead{GradedModule}{GRMOD} \pagepic{ps/v102gradedmodule.ps}{GRMOD}{1.00} +<>= +)set break resume +)sys rm -f GradedModule.output +)spool GradedModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GradedModule +--R GradedModule(R: CommutativeRing,E: AbelianMonoid) is a category constructor +--R Abbreviation for GradedModule is GRMOD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for GRMOD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R degree : % -> E hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GradedModule examples +==================================================================== + +See Also: +o )show GradedModule + +@ {\bf See:} \pageto{GradedAlgebra}{GRALG} @@ -5741,6 +7285,61 @@ digraph pic { \pagehead{HomogeneousAggregate}{HOAGG} \pagepic{ps/v102homogeneousaggregate.ps}{HOAGG}{1.00} +<>= +)set break resume +)sys rm -f HomogeneousAggregate.output +)spool HomogeneousAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show HomogeneousAggregate +--R HomogeneousAggregate S: Type is a category constructor +--R Abbreviation for HomogeneousAggregate is HOAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for HOAGG +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R map : ((S -> S),%) -> % sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +HomogeneousAggregate examples +==================================================================== + +See Also: +o )show HomogeneousAggregate + +@ {\bf See:} \pageto{BagAggregate}{BGAGG} @@ -5986,6 +7585,42 @@ digraph pic { \pagehead{IndexedDirectProductCategory}{IDPC} \pagepic{ps/v102liouvillianfunctioncategory.ps}{IDPC}{1.00} +<>= +)set break resume +)sys rm -f IndexedDirectProductCategory.output +)spool IndexedDirectProductCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedDirectProductCategory +--R IndexedDirectProductCategory(A: SetCategory,S: OrderedSet) is a category constructor +--R Abbreviation for IndexedDirectProductCategory is IDPC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for IDPC +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A leadingSupport : % -> S +--R map : ((A -> A),%) -> % monomial : (A,S) -> % +--R reductum : % -> % ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedDirectProductCategory examples +==================================================================== + +See Also: +o )show IndexedDirectProductCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -6106,6 +7741,56 @@ digraph pic { \pagehead{LiouvillianFunctionCategory}{LFCAT} \pagepic{ps/v102liouvillianfunctioncategory.ps}{LFCAT}{0.60} +<>= +)set break resume +)sys rm -f LiouvillianFunctionCategory.output +)spool LiouvillianFunctionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LiouvillianFunctionCategory +--R LiouvillianFunctionCategory is a category constructor +--R Abbreviation for LiouvillianFunctionCategory is LFCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LFCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?**? : (%,%) -> % Ci : % -> % +--R Ei : % -> % Si : % -> % +--R acos : % -> % acosh : % -> % +--R acot : % -> % acoth : % -> % +--R acsc : % -> % acsch : % -> % +--R asec : % -> % asech : % -> % +--R asin : % -> % asinh : % -> % +--R atan : % -> % atanh : % -> % +--R cos : % -> % cosh : % -> % +--R cot : % -> % coth : % -> % +--R csc : % -> % csch : % -> % +--R dilog : % -> % erf : % -> % +--R exp : % -> % integral : (%,Symbol) -> % +--R li : % -> % log : % -> % +--R pi : () -> % sec : % -> % +--R sech : % -> % sin : % -> % +--R sinh : % -> % tan : % -> % +--R tanh : % -> % +--R integral : (%,SegmentBinding %) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LiouvillianFunctionCategory examples +==================================================================== + +See Also: +o )show LiouvillianFunctionCategory + +@ {\bf See:} \pagefrom{PrimitiveFunctionCategory}{PRIMCAT} @@ -6292,6 +7977,43 @@ digraph pic { \pagehead{Monad}{MONAD} \pagepic{ps/v102monad.ps}{MONAD}{0.70} +<>= +)set break resume +)sys rm -f Monad.output +)spool Monad.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Monad +--R Monad is a category constructor +--R Abbreviation for Monad is MONAD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONAD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R leftPower : (%,PositiveInteger) -> % +--R rightPower : (%,PositiveInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Monad examples +==================================================================== + +See Also: +o )show Monad + +@ {\bf See:} \pageto{MonadWithUnit}{MONADWU} @@ -6434,6 +8156,44 @@ digraph pic { \pagehead{NumericalIntegrationCategory}{NUMINT} \pagepic{ps/v102numericalintegrationcategory.ps}{NUMINT}{1.00} +<>= +)set break resume +)sys rm -f NumericalIntegrationCategory.output +)spool NumericalIntegrationCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NumericalIntegrationCategory +--R NumericalIntegrationCategory is a category constructor +--R Abbreviation for NumericalIntegrationCategory is NUMINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for NUMINT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NumericalIntegrationCategory examples +==================================================================== + +See Also: +o )show NumericalIntegrationCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -6592,6 +8352,44 @@ digraph pic { \pagehead{NumericalOptimizationCategory}{OPTCAT} \pagepic{ps/v102numericaloptimizationcategory.ps}{OPTCAT}{1.00} +<>= +)set break resume +)sys rm -f NumericalOptimizationCategory.output +)spool NumericalOptimizationCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NumericalOptimizationCategory +--R NumericalOptimizationCategory is a category constructor +--R Abbreviation for NumericalOptimizationCategory is OPTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OPTCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NumericalOptimizationCategory examples +==================================================================== + +See Also: +o )show NumericalOptimizationCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -6744,6 +8542,42 @@ digraph pic { \pagehead{OrdinaryDifferentialEquationsSolverCategory}{ODECAT} \pagepic{ps/v102ordinarydifferentialequationssolvercategory.ps}{ODECAT}{1.00} +<>= +)set break resume +)sys rm -f OrdinaryDifferentialEquationsSolverCategory.output +)spool OrdinaryDifferentialEquationsSolverCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrdinaryDifferentialEquationsSolverCategory +--R OrdinaryDifferentialEquationsSolverCategory is a category constructor +--R Abbreviation for OrdinaryDifferentialEquationsSolverCategory is ODECAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ODECAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrdinaryDifferentialEquationsSolverCategory examples +==================================================================== + +See Also: +o )show OrdinaryDifferentialEquationsSolverCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -6877,6 +8711,43 @@ digraph pic { \pagehead{OrderedSet}{ORDSET} \pagepic{ps/v102orderedset.ps}{ORDSET}{1.00} +<>= +)set break resume +)sys rm -f OrderedSet.output +)spool OrderedSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedSet +--R OrderedSet is a category constructor +--R Abbreviation for OrderedSet is ORDSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ORDSET +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedSet examples +==================================================================== + +See Also: +o )show OrderedSet + +@ {\bf See:} \pageto{BitAggregate}{BTAGG} @@ -7017,6 +8888,42 @@ digraph pic { \pagehead{PartialDifferentialEquationsSolverCategory}{PDECAT} \pagepic{ps/v102partialdifferentialequationssolvercategory.ps}{PDECAT}{1.00} +<>= +)set break resume +)sys rm -f PartialDifferentialEquationsSolverCategory.output +)spool PartialDifferentialEquationsSolverCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PartialDifferentialEquationsSolverCategory +--R PartialDifferentialEquationsSolverCategory is a category constructor +--R Abbreviation for PartialDifferentialEquationsSolverCategory is PDECAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PDECAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R PDESolve : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PartialDifferentialEquationsSolverCategory examples +==================================================================== + +See Also: +o )show PartialDifferentialEquationsSolverCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -7179,6 +9086,41 @@ digraph pic { \pagehead{PatternMatchable}{PATMAB} \pagepic{ps/v102patternmatchable.ps}{PATMAB}{1.00} +<>= +)set break resume +)sys rm -f PatternMatchable.output +)spool PatternMatchable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PatternMatchable +--R PatternMatchable S: SetCategory is a category constructor +--R Abbreviation for PatternMatchable is PATMAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PATMAB +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R patternMatch : (%,Pattern S,PatternMatchResult(S,%)) -> PatternMatchResult(S,%) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PatternMatchable examples +==================================================================== + +See Also: +o )show PatternMatchable + +@ {\bf See:} \pageto{RealNumberSystem}{RNS} @@ -7284,6 +9226,48 @@ digraph pic { \pagehead{RealRootCharacterizationCategory}{RRCC} \pagepic{ps/v102realrootcharacterizationcategory.ps}{RRCC}{0.60} +<>= +)set break resume +)sys rm -f RealRootCharacterizationCategory.output +)spool RealRootCharacterizationCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RealRootCharacterizationCategory +--R RealRootCharacterizationCategory(TheField: Join(OrderedRing,Field),ThePols: UnivariatePolynomialCategory t#1) is a category constructor +--R Abbreviation for RealRootCharacterizationCategory is RRCC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RRCC +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean allRootsOf : ThePols -> List % +--R coerce : % -> OutputForm definingPolynomial : % -> ThePols +--R hash : % -> SingleInteger latex : % -> String +--R sign : (ThePols,%) -> Integer zero? : (ThePols,%) -> Boolean +--R ?~=? : (%,%) -> Boolean +--R approximate : (ThePols,%,TheField) -> TheField +--R negative? : (ThePols,%) -> Boolean +--R positive? : (ThePols,%) -> Boolean +--R recip : (ThePols,%) -> Union(ThePols,"failed") +--R relativeApprox : (ThePols,%,TheField) -> TheField +--R rootOf : (ThePols,PositiveInteger) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RealRootCharacterizationCategory examples +==================================================================== + +See Also: +o )show RealRootCharacterizationCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -7470,6 +9454,43 @@ digraph pic { \pagehead{SegmentExpansionCategory}{SEGXCAT} \pagepic{ps/v102segmentexpansioncategory.ps}{SEGXCAT}{0.75} +<>= +)set break resume +)sys rm -f SegmentExpansionCategory.output +)spool SegmentExpansionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SegmentExpansionCategory +--R SegmentExpansionCategory(S: OrderedRing,L: StreamAggregate t#1) is a category constructor +--R Abbreviation for SegmentExpansionCategory is SEGXCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SEGXCAT +--R +--R------------------------------- Operations -------------------------------- +--R BY : (%,Integer) -> % ?..? : (S,S) -> % +--R convert : S -> % expand : % -> L +--R expand : List % -> L hi : % -> S +--R high : % -> S incr : % -> Integer +--R lo : % -> S low : % -> S +--R map : ((S -> S),%) -> L segment : (S,S) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SegmentExpansionCategory examples +==================================================================== + +See Also: +o )show SegmentExpansionCategory + +@ {\bf See:} \pagefrom{SegmentCategory}{SEGCAT} @@ -7590,7 +9611,6 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{SemiGroup}{SGROUP} \pagepic{ps/v102semigroup.ps}{SGROUP}{0.75} - A Semigroup is defined as a set $S$ with a binary multiplicative operator ``*''. A Semigroup $G(S,*)$ is: \begin{itemize} @@ -7599,6 +9619,42 @@ operator ``*''. A Semigroup $G(S,*)$ is: \item associative. $\forall a,b,c \in S, a*(b*c) = (a*b)*c$ \end{itemize} +<>= +)set break resume +)sys rm -f SemiGroup.output +)spool SemiGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SemiGroup +--R SemiGroup is a category constructor +--R Abbreviation for SemiGroup is SGROUP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SGROUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?=? : (%,%) -> Boolean ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SemiGroup examples +==================================================================== + +See Also: +o )show SemiGroup + +@ + {\bf See:} \pageto{FunctionSpace}{FS} @@ -7849,6 +9905,53 @@ digraph pic { \pagehead{SExpressionCategory}{SEXCAT} \pagepic{ps/v102sexpressioncategory.ps}{SEXCAT}{0.60} +<>= +)set break resume +)sys rm -f SExpressionCategory.output +)spool SExpressionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SExpressionCategory +--R SExpressionCategory(Str: SetCategory,Sym: SetCategory,Int: SetCategory,Flt: SetCategory,Expr: SetCategory) is a category constructor +--R Abbreviation for SExpressionCategory is SEXCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SEXCAT +--R +--R------------------------------- Operations -------------------------------- +--R #? : % -> Integer ?=? : (%,%) -> Boolean +--R atom? : % -> Boolean car : % -> % +--R cdr : % -> % coerce : % -> OutputForm +--R convert : Expr -> % convert : Flt -> % +--R convert : Int -> % convert : Sym -> % +--R convert : Str -> % convert : List % -> % +--R destruct : % -> List % ?.? : (%,List Integer) -> % +--R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean +--R expr : % -> Expr float : % -> Flt +--R float? : % -> Boolean hash : % -> SingleInteger +--R integer : % -> Int integer? : % -> Boolean +--R latex : % -> String list? : % -> Boolean +--R null? : % -> Boolean pair? : % -> Boolean +--R string : % -> Str string? : % -> Boolean +--R symbol : % -> Sym symbol? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SExpressionCategory examples +==================================================================== + +See Also: +o )show SExpressionCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -8046,6 +10149,41 @@ digraph pic { \pagehead{StepThrough}{STEP} \pagepic{ps/v102stepthrough.ps}{STEP}{1.00} +<>= +)set break resume +)sys rm -f StepThrough.output +)spool StepThrough.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show StepThrough +--R StepThrough is a category constructor +--R Abbreviation for StepThrough is STEP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for STEP +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger init : () -> % +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R nextItem : % -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +StepThrough examples +==================================================================== + +See Also: +o )show StepThrough + +@ {\bf See:} \pageto{FiniteFieldCategory}{FFIELDC} @@ -8155,6 +10293,73 @@ digraph pic { \pagehead{ThreeSpaceCategory}{SPACEC} \pagepic{ps/v102threespacecategory.ps}{SPACEC}{1.00} +<>= +)set break resume +)sys rm -f ThreeSpaceCategory.output +)spool ThreeSpaceCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ThreeSpaceCategory +--R ThreeSpaceCategory R: Ring is a category constructor +--R Abbreviation for ThreeSpaceCategory is SPACEC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SPACEC +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean check : % -> % +--R closedCurve : % -> List Point R closedCurve : List Point R -> % +--R closedCurve? : % -> Boolean coerce : % -> OutputForm +--R components : % -> List % composite : List % -> % +--R composites : % -> List % copy : % -> % +--R create3Space : SubSpace(3,R) -> % create3Space : () -> % +--R curve : % -> List Point R curve : List Point R -> % +--R curve : (%,List List R) -> % curve : (%,List Point R) -> % +--R curve? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lp : % -> List Point R +--R merge : (%,%) -> % merge : List % -> % +--R mesh : % -> List List Point R mesh : List List Point R -> % +--R mesh? : % -> Boolean point : % -> Point R +--R point : Point R -> % point : (%,List R) -> % +--R point : (%,Point R) -> % point? : % -> Boolean +--R polygon : % -> List Point R polygon : List Point R -> % +--R polygon : (%,List List R) -> % polygon : (%,List Point R) -> % +--R polygon? : % -> Boolean subspace : % -> SubSpace(3,R) +--R ?~=? : (%,%) -> Boolean +--R closedCurve : (%,List List R) -> % +--R closedCurve : (%,List Point R) -> % +--R enterPointData : (%,List Point R) -> NonNegativeInteger +--R lllip : % -> List List List NonNegativeInteger +--R lllp : % -> List List List Point R +--R llprop : % -> List List SubSpaceComponentProperty +--R lprop : % -> List SubSpaceComponentProperty +--R mesh : (List List Point R,Boolean,Boolean) -> % +--R mesh : (%,List List List R,Boolean,Boolean) -> % +--R mesh : (%,List List Point R,Boolean,Boolean) -> % +--R mesh : (%,List List List R,List SubSpaceComponentProperty,SubSpaceComponentProperty) -> % +--R mesh : (%,List List Point R,List SubSpaceComponentProperty,SubSpaceComponentProperty) -> % +--R modifyPointData : (%,NonNegativeInteger,Point R) -> % +--R numberOfComponents : % -> NonNegativeInteger +--R numberOfComposites : % -> NonNegativeInteger +--R objects : % -> Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger) +--R point : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ThreeSpaceCategory examples +==================================================================== + +See Also: +o )show ThreeSpaceCategory + +@ {\bf See:} \pagefrom{SetCategory}{SETCAT} @@ -8607,6 +10812,43 @@ digraph pic { \pagehead{AbelianMonoid}{ABELMON} \pagepic{ps/v102abelianmonoid.ps}{ABELMON}{0.75} +<>= +)set break resume +)sys rm -f AbelianMonoid.output +)spool AbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AbelianMonoid +--R AbelianMonoid is a category constructor +--R Abbreviation for AbelianMonoid is ABELMON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ABELMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AbelianMonoid examples +==================================================================== + +See Also: +o )show AbelianMonoid + +@ {\bf See:} \pageto{CancellationAbelianMonoid}{CABMON} @@ -8977,6 +11219,63 @@ digraph pic { \pagehead{BagAggregate}{BGAGG} \pagepic{ps/v102bagaggregate.ps}{BGAGG}{1.00} +<>= +)set break resume +)sys rm -f BagAggregate.output +)spool BagAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BagAggregate +--R BagAggregate S: Type is a category constructor +--R Abbreviation for BagAggregate is BGAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BGAGG +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % copy : % -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R insert! : (S,%) -> % inspect : % -> S +--R map : ((S -> S),%) -> % sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BagAggregate examples +==================================================================== + +See Also: +o )show BagAggregate + +@ {\bf See:} \pageto{DictionaryOperations}{DIOPS} @@ -9154,6 +11453,45 @@ digraph pic { \pagehead{CachableSet}{CACHSET} \pagepic{ps/v102cachableset.ps}{CACHSET}{1.00} +<>= +)set break resume +)sys rm -f CachableSet.output +)spool CachableSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CachableSet +--R CachableSet is a category constructor +--R Abbreviation for CachableSet is CACHSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CACHSET +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R position : % -> NonNegativeInteger +--R setPosition : (%,NonNegativeInteger) -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CachableSet examples +==================================================================== + +See Also: +o )show CachableSet + +@ {\bf See:} \pagefrom{OrderedSet}{ORDSET} @@ -9259,6 +11597,71 @@ digraph pic { \pagehead{Collection}{CLAGG} \pagepic{ps/v102collection.ps}{CLAGG}{1.00} +<>= +)set break resume +)sys rm -f Collection.output +)spool Collection.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Collection +--R Collection S: Type is a category constructor +--R Abbreviation for Collection is CLAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CLAGG +--R +--R------------------------------- Operations -------------------------------- +--R construct : List S -> % copy : % -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean map : ((S -> S),%) -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Collection examples +==================================================================== + +See Also: +o )show Collection + +@ {\bf See:} \pageto{DictionaryOperations}{DIOPS} @@ -9522,6 +11925,49 @@ digraph pic { \pagehead{DifferentialVariableCategory}{DVARCAT} \pagepic{ps/v102differentialvariablecategory.ps}{DVARCAT}{1.00} +<>= +)set break resume +)sys rm -f DifferentialVariableCategory.output +)spool DifferentialVariableCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DifferentialVariableCategory +--R DifferentialVariableCategory S: OrderedSet is a category constructor +--R Abbreviation for DifferentialVariableCategory is DVARCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DVARCAT +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : S -> % +--R coerce : % -> OutputForm differentiate : % -> % +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R order : % -> NonNegativeInteger retract : % -> S +--R variable : % -> S weight : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R differentiate : (%,NonNegativeInteger) -> % +--R makeVariable : (S,NonNegativeInteger) -> % +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DifferentialVariableCategory examples +==================================================================== + +See Also: +o )show DifferentialVariableCategory + +@ {\bf See:} \pagefrom{OrderedSet}{ORDSET} @@ -9759,6 +12205,79 @@ digraph pic { \pagehead{ExpressionSpace}{ES} \pagepic{ps/v102expressionspace.ps}{ES}{0.35} +<>= +)set break resume +)sys rm -f ExpressionSpace.output +)spool ExpressionSpace.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ExpressionSpace +--R ExpressionSpace is a category constructor +--R Abbreviation for ExpressionSpace is ES +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ES +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean belong? : BasicOperator -> Boolean +--R box : List % -> % box : % -> % +--R coerce : Kernel % -> % coerce : % -> OutputForm +--R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,Kernel %,%) -> % freeOf? : (%,Symbol) -> Boolean +--R freeOf? : (%,%) -> Boolean hash : % -> SingleInteger +--R height : % -> NonNegativeInteger is? : (%,Symbol) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel % +--R latex : % -> String map : ((% -> %),Kernel %) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R paren : List % -> % paren : % -> % +--R retract : % -> Kernel % subst : (%,Equation %) -> % +--R tower : % -> List Kernel % ?~=? : (%,%) -> Boolean +--R definingPolynomial : % -> % if $ has RING +--R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Kernel %,List %) -> % +--R even? : % -> Boolean if $ has RETRACT INT +--R is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,List %) -> % +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R odd? : % -> Boolean if $ has RETRACT INT +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R retractIfCan : % -> Union(Kernel %,"failed") +--R subst : (%,List Kernel %,List %) -> % +--R subst : (%,List Equation %) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ExpressionSpace examples +==================================================================== + +See Also: +o )show ExpressionSpace + +@ {\bf See:} \pageto{FunctionSpace}{FS} @@ -10288,6 +12807,46 @@ digraph pic { \pagehead{GradedAlgebra}{GRALG} \pagepic{ps/v102gradedalgebra.ps}{GRALG}{0.75} +<>= +)set break resume +)sys rm -f GradedAlgebra.output +)spool GradedAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GradedAlgebra +--R GradedAlgebra(R: CommutativeRing,E: AbelianMonoid) is a category constructor +--R Abbreviation for GradedAlgebra is GRALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for GRALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R coerce : R -> % coerce : % -> OutputForm +--R degree : % -> E hash : % -> SingleInteger +--R latex : % -> String product : (%,%) -> % +--R retract : % -> R ?~=? : (%,%) -> Boolean +--R retractIfCan : % -> Union(R,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GradedAlgebra examples +==================================================================== + +See Also: +o )show GradedAlgebra + +@ {\bf See:} \pagefrom{GradedModule}{GRMOD} @@ -10445,6 +13004,72 @@ digraph pic { \pagehead{IndexedAggregate}{IXAGG} \pagepic{ps/v102indexedaggregate.ps}{IXAGG}{0.90} +<>= +)set break resume +)sys rm -f IndexedAggregate.output +)spool IndexedAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedAggregate +--R IndexedAggregate(Index: SetCategory,Entry: Type) is a category constructor +--R Abbreviation for IndexedAggregate is IXAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for IXAGG +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % ?.? : (%,Index) -> Entry +--R elt : (%,Index,Entry) -> Entry empty : () -> % +--R empty? : % -> Boolean entries : % -> List Entry +--R eq? : (%,%) -> Boolean index? : (Index,%) -> Boolean +--R indices : % -> List Index map : ((Entry -> Entry),%) -> % +--R qelt : (%,Index) -> Entry sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if Entry has SETCAT +--R count : (Entry,%) -> NonNegativeInteger if Entry has SETCAT and $ has finiteAggregate +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R first : % -> Entry if Index has ORDSET +--R hash : % -> SingleInteger if Entry has SETCAT +--R latex : % -> String if Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Index if Index has ORDSET +--R member? : (Entry,%) -> Boolean if Entry has SETCAT and $ has finiteAggregate +--R members : % -> List Entry if $ has finiteAggregate +--R minIndex : % -> Index if Index has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Entry if $ has finiteAggregate +--R qsetelt! : (%,Index,Entry) -> Entry if $ has shallowlyMutable +--R setelt : (%,Index,Entry) -> Entry if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Index,Index) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if Entry has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedAggregate examples +==================================================================== + +See Also: +o )show IndexedAggregate + +@ {\bf See:} \pageto{DirectProductCategory}{DIRPCAT} @@ -10727,6 +13352,49 @@ digraph pic { \pagehead{MonadWithUnit}{MONADWU} \pagepic{ps/v102monadwithunit.ps}{MONADWU}{0.75} +<>= +)set break resume +)sys rm -f MonadWithUnit.output +)spool MonadWithUnit.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MonadWithUnit +--R MonadWithUnit is a category constructor +--R Abbreviation for MonadWithUnit is MONADWU +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONADWU +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R leftPower : (%,NonNegativeInteger) -> % +--R leftPower : (%,PositiveInteger) -> % +--R leftRecip : % -> Union(%,"failed") +--R rightPower : (%,NonNegativeInteger) -> % +--R rightPower : (%,PositiveInteger) -> % +--R rightRecip : % -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MonadWithUnit examples +==================================================================== + +See Also: +o )show MonadWithUnit + +@ {\bf See:} \pageto{NonAssociativeRing}{NASRING} @@ -10907,6 +13575,45 @@ digraph pic { \pagehead{Monoid}{MONOID} \pagepic{ps/v102monoid.ps}{MONOID}{0.75} +<>= +)set break resume +)sys rm -f Monoid.output +)spool Monoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Monoid +--R Monoid is a category constructor +--R Abbreviation for Monoid is MONOID +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONOID +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Monoid examples +==================================================================== + +See Also: +o )show Monoid + +@ {\bf See:} \pageto{FunctionSpace}{FS} @@ -11065,6 +13772,45 @@ digraph pic { \pagehead{OrderedFinite}{ORDFIN} \pagepic{ps/v102orderedfinite.ps}{ORDFIN}{1.00} +<>= +)set break resume +)sys rm -f OrderedFinite.output +)spool OrderedFinite.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedFinite +--R OrderedFinite is a category constructor +--R Abbreviation for OrderedFinite is ORDFIN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ORDFIN +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger index : PositiveInteger -> % +--R latex : % -> String lookup : % -> PositiveInteger +--R max : (%,%) -> % min : (%,%) -> % +--R random : () -> % size : () -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedFinite examples +==================================================================== + +See Also: +o )show OrderedFinite + +@ {\bf See:} \pagefrom{Finite}{FINITE} @@ -11648,6 +14394,70 @@ digraph pic { \pagehead{RecursiveAggregate}{RCAGG} \pagepic{ps/v102recursiveaggregate.ps}{RCAGG}{1.00} +<>= +)set break resume +)sys rm -f RecursiveAggregate.output +)spool RecursiveAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RecursiveAggregate +--R RecursiveAggregate S: Type is a category constructor +--R Abbreviation for RecursiveAggregate is RCAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RCAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R leaf? : % -> Boolean leaves : % -> List S +--R map : ((S -> S),%) -> % nodes : % -> List % +--R sample : () -> % value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RecursiveAggregate examples +==================================================================== + +See Also: +o )show RecursiveAggregate + +@ {\bf See:} \pageto{BinaryRecursiveAggregate}{BRAGG} @@ -11881,6 +14691,73 @@ be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa. +<>= +)set break resume +)sys rm -f TwoDimensionalArrayCategory.output +)spool TwoDimensionalArrayCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TwoDimensionalArrayCategory +--R TwoDimensionalArrayCategory(R: Type,Row: FiniteLinearAggregate t#1,Col: FiniteLinearAggregate t#1) is a category constructor +--R Abbreviation for TwoDimensionalArrayCategory is ARR2CAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ARR2CAT +--R +--R------------------------------- Operations -------------------------------- +--R column : (%,Integer) -> Col copy : % -> % +--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean fill! : (%,R) -> % +--R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List R qelt : (%,Integer,Integer) -> R +--R row : (%,Integer) -> Row sample : () -> % +--R setRow! : (%,Integer,Row) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate +--R members : % -> List R if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,NonNegativeInteger,R) -> % +--R qsetelt! : (%,Integer,Integer,R) -> R +--R setColumn! : (%,Integer,Col) -> % +--R setelt : (%,Integer,Integer,R) -> R +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TwoDimensionalArrayCategory examples +==================================================================== + +See Also: +o )show TwoDimensionalArrayCategory + +@ + {\bf See:} \pageto{MatrixCategory}{MATCAT} @@ -12424,6 +15301,76 @@ digraph pic { \pagehead{BinaryRecursiveAggregate}{BRAGG} \pagepic{ps/v102binaryrecursiveaggregate.ps}{BRAGG}{1.00} +<>= +)set break resume +)sys rm -f BinaryRecursiveAggregate.output +)spool BinaryRecursiveAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BinaryRecursiveAggregate +--R BinaryRecursiveAggregate S: Type is a category constructor +--R Abbreviation for BinaryRecursiveAggregate is BRAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BRAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.right : (%,right) -> % ?.left : (%,left) -> % +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R leaf? : % -> Boolean leaves : % -> List S +--R left : % -> % map : ((S -> S),%) -> % +--R nodes : % -> List % right : % -> % +--R sample : () -> % value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BinaryRecursiveAggregate examples +==================================================================== + +See Also: +o )show BinaryRecursiveAggregate + +@ {\bf See:} \pageto{BinaryTreeCategory}{BTCAT} @@ -12719,6 +15666,44 @@ digraph pic { \pagehead{CancellationAbelianMonoid}{CABMON} \pagepic{ps/v102cancellationabelianmonoid.ps}{CABMON}{0.75} +<>= +)set break resume +)sys rm -f CancellationAbelianMonoid.output +)spool CancellationAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CancellationAbelianMonoid +--R CancellationAbelianMonoid is a category constructor +--R Abbreviation for CancellationAbelianMonoid is CABMON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CABMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CancellationAbelianMonoid examples +==================================================================== + +See Also: +o )show CancellationAbelianMonoid + +@ {\bf See:} \pageto{AbelianGroup}{ABELGRP} @@ -12844,6 +15829,77 @@ digraph pic { \pagehead{DictionaryOperations}{DIOPS} \pagepic{ps/v102dictionaryoperations.ps}{DIOPS}{1.00} +<>= +)set break resume +)sys rm -f DictionaryOperations.output +)spool DictionaryOperations.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DictionaryOperations +--R DictionaryOperations S: SetCategory is a category constructor +--R Abbreviation for DictionaryOperations is DIOPS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIOPS +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % construct : List S -> % +--R copy : % -> % dictionary : List S -> % +--R dictionary : () -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extract! : % -> S insert! : (S,%) -> % +--R inspect : % -> S map : ((S -> S),%) -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DictionaryOperations examples +==================================================================== + +See Also: +o )show DictionaryOperations + +@ {\bf See:} \pageto{Dictionary}{DIAGG} @@ -13082,6 +16138,76 @@ digraph pic { \pagehead{DoublyLinkedAggregate}{DLAGG} \pagepic{ps/v102doublylinkedaggregate.ps}{DLAGG}{1.00} +<>= +)set break resume +)sys rm -f DoublyLinkedAggregate.output +)spool DoublyLinkedAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DoublyLinkedAggregate +--R DoublyLinkedAggregate S: Type is a category constructor +--R Abbreviation for DoublyLinkedAggregate is DLAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DLAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R head : % -> % last : % -> S +--R leaf? : % -> Boolean leaves : % -> List S +--R map : ((S -> S),%) -> % next : % -> % +--R nodes : % -> List % previous : % -> % +--R sample : () -> % tail : % -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R concat! : (%,%) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setnext! : (%,%) -> % if $ has shallowlyMutable +--R setprevious! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DoublyLinkedAggregate examples +==================================================================== + +See Also: +o )show DoublyLinkedAggregate + +@ {\bf See:} \pagefrom{RecursiveAggregate}{RCAGG} @@ -13301,6 +16427,48 @@ digraph pic { \pagehead{Group}{GROUP} \pagepic{ps/v102group.ps}{GROUP}{0.65} +<>= +)set break resume +)sys rm -f Group.output +)spool Group.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Group +--R Group is a category constructor +--R Abbreviation for Group is GROUP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for GROUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R conjugate : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Group examples +==================================================================== + +See Also: +o )show Group + +@ {\bf See:} \pageto{FunctionSpace}{FS} @@ -13479,6 +16647,89 @@ digraph pic { \pagehead{LinearAggregate}{LNAGG} \pagepic{ps/v102linearaggregate.ps}{LNAGG}{0.90} +<>= +)set break resume +)sys rm -f LinearAggregate.output +)spool LinearAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LinearAggregate +--R LinearAggregate S: Type is a category constructor +--R Abbreviation for LinearAggregate is LNAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LNAGG +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LinearAggregate examples +==================================================================== + +See Also: +o )show LinearAggregate + +@ {\bf See:} \pageto{ExtensibleLinearAggregate}{ELAGG} @@ -13784,6 +17035,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{MatrixCategory}{MATCAT} \pagepic{ps/v102matrixcategory.ps}{MATCAT}{0.60} + <>= )set break resume )sys rm -f MatrixCategory.output @@ -15996,6 +19248,46 @@ digraph pic { \pagehead{OrderedAbelianSemiGroup}{OASGP} \pagepic{ps/v102orderedabeliansemigroup.ps}{OASGP}{0.75} +<>= +)set break resume +)sys rm -f OrderedAbelianSemiGroup.output +)spool OrderedAbelianSemiGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedAbelianSemiGroup +--R OrderedAbelianSemiGroup is a category constructor +--R Abbreviation for OrderedAbelianSemiGroup is OASGP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OASGP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedAbelianSemiGroup examples +==================================================================== + +See Also: +o )show OrderedAbelianSemiGroup + +@ {\bf See:} \pageto{OrderedAbelianMonoid}{OAMON} @@ -16133,6 +19425,48 @@ digraph pic { \pagehead{OrderedMonoid}{ORDMON} \pagepic{ps/v102orderedmonoid.ps}{ORDMON}{0.75} +<>= +)set break resume +)sys rm -f OrderedMonoid.output +)spool OrderedMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedMonoid +--R OrderedMonoid is a category constructor +--R Abbreviation for OrderedMonoid is ORDMON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ORDMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedMonoid examples +==================================================================== + +See Also: +o )show OrderedMonoid + +@ {\bf See:} \pagefrom{Monoid}{MONOID} @@ -16277,6 +19611,85 @@ digraph pic { \pagehead{PolynomialSetCategory}{PSETCAT} \pagepic{ps/v102polynomialsetcategory.ps}{PSETCAT}{0.30} +<>= +)set break resume +)sys rm -f PolynomialSetCategory.output +)spool PolynomialSetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PolynomialSetCategory +--R PolynomialSetCategory(R: Ring,E: OrderedAbelianMonoidSup,VarSet: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for PolynomialSetCategory is PSETCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PSETCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> List P +--R coerce : % -> OutputForm collect : (%,VarSet) -> % +--R collectUnder : (%,VarSet) -> % collectUpper : (%,VarSet) -> % +--R construct : List P -> % copy : % -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R latex : % -> String mainVariables : % -> List VarSet +--R map : ((P -> P),%) -> % mvar : % -> VarSet +--R retract : List P -> % sample : () -> % +--R trivialIdeal? : % -> Boolean variables : % -> List VarSet +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R less? : (%,NonNegativeInteger) -> Boolean +--R mainVariable? : (VarSet,%) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,VarSet) -> Record(under: %,floor: %,upper: %) +--R triangular? : % -> Boolean if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PolynomialSetCategory examples +==================================================================== + +See Also: +o )show PolynomialSetCategory + +@ {\bf See:} \pageto{TriangularSetCategory}{TSETCAT} @@ -16881,6 +20294,65 @@ digraph pic { \pagehead{PriorityQueueAggregate}{PRQAGG} \pagepic{ps/v102priorityqueueaggregate.ps}{PRQAGG}{1.00} +<>= +)set break resume +)sys rm -f PriorityQueueAggregate.output +)spool PriorityQueueAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PriorityQueueAggregate +--R PriorityQueueAggregate S: OrderedSet is a category constructor +--R Abbreviation for PriorityQueueAggregate is PRQAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PRQAGG +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % copy : % -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R insert! : (S,%) -> % inspect : % -> S +--R map : ((S -> S),%) -> % max : % -> S +--R merge : (%,%) -> % merge! : (%,%) -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PriorityQueueAggregate examples +==================================================================== + +See Also: +o )show PriorityQueueAggregate + +@ {\bf See:} \pageto{OrderedMultisetAggregate}{OMSAGG} @@ -17058,6 +20530,66 @@ digraph pic { \pagehead{QueueAggregate}{QUAGG} \pagepic{ps/v102queueaggregate.ps}{QUAGG}{1.00} +<>= +)set break resume +)sys rm -f QueueAggregate.output +)spool QueueAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show QueueAggregate +--R QueueAggregate S: Type is a category constructor +--R Abbreviation for QueueAggregate is QUAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for QUAGG +--R +--R------------------------------- Operations -------------------------------- +--R back : % -> S bag : List S -> % +--R copy : % -> % dequeue! : % -> S +--R empty : () -> % empty? : % -> Boolean +--R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean +--R extract! : % -> S front : % -> S +--R insert! : (S,%) -> % inspect : % -> S +--R length : % -> NonNegativeInteger map : ((S -> S),%) -> % +--R rotate! : % -> % sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +QueueAggregate examples +==================================================================== + +See Also: +o )show QueueAggregate + +@ {\bf See:} \pageto{DequeueAggregate}{DQAGG} @@ -17248,6 +20780,75 @@ digraph pic { \pagehead{SetAggregate}{SETAGG} \pagepic{ps/v102setaggregate.ps}{SETAGG}{0.90} +<>= +)set break resume +)sys rm -f SetAggregate.output +)spool SetAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SetAggregate +--R SetAggregate S: SetCategory is a category constructor +--R Abbreviation for SetAggregate is SETAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SETAGG +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R brace : List S -> % brace : () -> % +--R coerce : % -> OutputForm construct : List S -> % +--R copy : % -> % difference : (%,S) -> % +--R difference : (%,%) -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger intersect : (%,%) -> % +--R latex : % -> String map : ((S -> S),%) -> % +--R sample : () -> % set : List S -> % +--R set : () -> % subset? : (%,%) -> Boolean +--R union : (S,%) -> % union : (%,S) -> % +--R union : (%,%) -> % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R symmetricDifference : (%,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SetAggregate examples +==================================================================== + +See Also: +o )show SetAggregate + +@ {\bf See:} \pageto{FiniteSetAggregate}{FSAGG} @@ -17538,6 +21139,65 @@ digraph pic { \pagehead{StackAggregate}{SKAGG} \pagepic{ps/v102stackaggregate.ps}{SKAGG}{1.00} +<>= +)set break resume +)sys rm -f StackAggregate.output +)spool StackAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show StackAggregate +--R StackAggregate S: Type is a category constructor +--R Abbreviation for StackAggregate is SKAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SKAGG +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % copy : % -> % +--R depth : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extract! : % -> S insert! : (S,%) -> % +--R inspect : % -> S map : ((S -> S),%) -> % +--R pop! : % -> S push! : (S,%) -> S +--R sample : () -> % top : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +StackAggregate examples +==================================================================== + +See Also: +o )show StackAggregate + +@ {\bf See:} \pageto{DequeueAggregate}{DQAGG} @@ -17731,6 +21391,91 @@ digraph pic { \pagehead{UnaryRecursiveAggregate}{URAGG} \pagepic{ps/v102unaryrecursiveaggregate.ps}{URAGG}{1.00} +<>= +)set break resume +)sys rm -f UnaryRecursiveAggregate.output +)spool UnaryRecursiveAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnaryRecursiveAggregate +--R UnaryRecursiveAggregate S: Type is a category constructor +--R Abbreviation for UnaryRecursiveAggregate is URAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for URAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % concat : (S,%) -> % +--R concat : (%,%) -> % copy : % -> % +--R cycleEntry : % -> % cycleTail : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.last : (%,last) -> S ?.rest : (%,rest) -> % +--R ?.first : (%,first) -> S ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean first : % -> S +--R last : % -> S leaf? : % -> Boolean +--R leaves : % -> List S map : ((S -> S),%) -> % +--R nodes : % -> List % rest : % -> % +--R sample : () -> % second : % -> S +--R tail : % -> % third : % -> S +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R concat! : (%,S) -> % if $ has shallowlyMutable +--R concat! : (%,%) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R rest : (%,NonNegativeInteger) -> % +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnaryRecursiveAggregate examples +==================================================================== + +See Also: +o )show UnaryRecursiveAggregate + +@ {\bf See:} \pageto{StreamAggregate}{STAGG} @@ -18204,6 +21949,46 @@ digraph pic { \pagehead{AbelianGroup}{ABELGRP} \pagepic{ps/v102abeliangroup.ps}{ABELGRP}{0.75} +<>= +)set break resume +)sys rm -f AbelianGroup.output +)spool AbelianGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AbelianGroup +--R AbelianGroup is a category constructor +--R Abbreviation for AbelianGroup is ABELGRP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ABELGRP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AbelianGroup examples +==================================================================== + +See Also: +o )show AbelianGroup + +@ {\bf See:} \pageto{FiniteDivisorCategory}{FDIVCAT} @@ -18353,6 +22138,77 @@ digraph pic { \pagehead{BinaryTreeCategory}{BTCAT} \pagepic{ps/v102binarytreecategory.ps}{BTCAT}{1.00} +<>= +)set break resume +)sys rm -f BinaryTreeCategory.output +)spool BinaryTreeCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BinaryTreeCategory +--R BinaryTreeCategory S: SetCategory is a category constructor +--R Abbreviation for BinaryTreeCategory is BTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BTCAT +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.right : (%,right) -> % ?.left : (%,left) -> % +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R leaf? : % -> Boolean leaves : % -> List S +--R left : % -> % map : ((S -> S),%) -> % +--R node : (%,S,%) -> % nodes : % -> List % +--R right : % -> % sample : () -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BinaryTreeCategory examples +==================================================================== + +See Also: +o )show BinaryTreeCategory + +@ {\bf See:} \pagefrom{BinaryRecursiveAggregate}{BRAGG} @@ -18582,6 +22438,77 @@ digraph pic { \pagehead{Dictionary}{DIAGG} \pagepic{ps/v102dictionary.ps}{DIAGG}{1.00} +<>= +)set break resume +)sys rm -f Dictionary.output +)spool Dictionary.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Dictionary +--R Dictionary S: SetCategory is a category constructor +--R Abbreviation for Dictionary is DIAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIAGG +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % construct : List S -> % +--R copy : % -> % dictionary : List S -> % +--R dictionary : () -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extract! : % -> S insert! : (S,%) -> % +--R inspect : % -> S map : ((S -> S),%) -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Dictionary examples +==================================================================== + +See Also: +o )show Dictionary + +@ {\bf See:} \pageto{FiniteSetAggregate}{FSAGG} @@ -18812,6 +22739,73 @@ digraph pic { \pagehead{DequeueAggregate}{DQAGG} \pagepic{ps/v102dequeueaggregate.ps}{DQAGG}{1.00} +<>= +)set break resume +)sys rm -f DequeueAggregate.output +)spool DequeueAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DequeueAggregate +--R DequeueAggregate S: Type is a category constructor +--R Abbreviation for DequeueAggregate is DQAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DQAGG +--R +--R------------------------------- Operations -------------------------------- +--R back : % -> S bag : List S -> % +--R bottom! : % -> S copy : % -> % +--R depth : % -> NonNegativeInteger dequeue : List S -> % +--R dequeue : () -> % dequeue! : % -> S +--R empty : () -> % empty? : % -> Boolean +--R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean +--R extract! : % -> S extractBottom! : % -> S +--R extractTop! : % -> S front : % -> S +--R height : % -> NonNegativeInteger insert! : (S,%) -> % +--R insertBottom! : (S,%) -> S insertTop! : (S,%) -> S +--R inspect : % -> S length : % -> NonNegativeInteger +--R map : ((S -> S),%) -> % pop! : % -> S +--R push! : (S,%) -> S reverse! : % -> % +--R rotate! : % -> % sample : () -> % +--R top : % -> S top! : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DequeueAggregate examples +==================================================================== + +See Also: +o )show DequeueAggregate + +@ {\bf See:} \pagefrom{QueueAggregate}{QUAGG} @@ -19048,6 +23042,99 @@ digraph pic { \pagehead{ExtensibleLinearAggregate}{ELAGG} \pagepic{ps/v102extensiblelinearaggregate.ps}{ELAGG}{0.90} +<>= +)set break resume +)sys rm -f ExtensibleLinearAggregate.output +)spool ExtensibleLinearAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ExtensibleLinearAggregate +--R ExtensibleLinearAggregate S: Type is a category constructor +--R Abbreviation for ExtensibleLinearAggregate is ELAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ELAGG +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R concat! : (%,%) -> % concat! : (%,S) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % delete! : (%,Integer) -> % +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (%,%,Integer) -> % insert : (S,%,Integer) -> % +--R insert! : (%,%,Integer) -> % insert! : (S,%,Integer) -> % +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R delete! : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R merge! : (%,%) -> % if S has ORDSET +--R merge! : (((S,S) -> Boolean),%,%) -> % +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : (S,%) -> % if S has SETCAT +--R remove! : ((S -> Boolean),%) -> % +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates! : % -> % if S has SETCAT +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ExtensibleLinearAggregate examples +==================================================================== + +See Also: +o )show ExtensibleLinearAggregate + +@ {\bf See:} \pageto{ListAggregate}{LSAGG} @@ -19346,6 +23433,109 @@ digraph pic { \pagehead{FiniteLinearAggregate}{FLAGG} \pagepic{ps/v102finitelinearaggregate.ps}{FLAGG}{0.90} +<>= +)set break resume +)sys rm -f FiniteLinearAggregate.output +)spool FiniteLinearAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteLinearAggregate +--R FiniteLinearAggregate S: Type is a category constructor +--R Abbreviation for FiniteLinearAggregate is FLAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FLAGG +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S reverse : % -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R merge : (%,%) -> % if S has ORDSET +--R merge : (((S,S) -> Boolean),%,%) -> % +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R position : (S,%) -> Integer if S has SETCAT +--R position : ((S -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if S has ORDSET +--R sort : (((S,S) -> Boolean),%) -> % +--R sort! : % -> % if S has ORDSET and $ has shallowlyMutable +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteLinearAggregate examples +==================================================================== + +See Also: +o )show FiniteLinearAggregate + +@ {\bf See:} \pageto{OneDimensionalArrayAggregate}{A1AGG} @@ -19695,6 +23885,52 @@ digraph pic { \pagehead{FreeAbelianMonoidCategory}{FAMONC} \pagepic{ps/v102freeabelianmonoidcategory.ps}{FAMONC}{0.50} +<>= +)set break resume +)sys rm -f FreeAbelianMonoidCategory.output +)spool FreeAbelianMonoidCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeAbelianMonoidCategory +--R FreeAbelianMonoidCategory(S: SetCategory,E: CancellationAbelianMonoid) is a category constructor +--R Abbreviation for FreeAbelianMonoidCategory is FAMONC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FAMONC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (E,S) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (S,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coefficient : (S,%) -> E coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String mapCoef : ((E -> E),%) -> % +--R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> E +--R nthFactor : (%,Integer) -> S retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R highCommonTerms : (%,%) -> % if E has OAMON +--R retractIfCan : % -> Union(S,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> List Record(gen: S,exp: E) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeAbelianMonoidCategory examples +==================================================================== + +See Also: +o )show FreeAbelianMonoidCategory + +@ {\bf See:} \pagefrom{CancellationAbelianMonoid}{CABMON} @@ -19882,6 +24118,79 @@ digraph pic { \pagehead{MultiDictionary}{MDAGG} \pagepic{ps/v102multidictionary.ps}{MDAGG}{0.90} +<>= +)set break resume +)sys rm -f MultiDictionary.output +)spool MultiDictionary.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MultiDictionary +--R MultiDictionary S: SetCategory is a category constructor +--R Abbreviation for MultiDictionary is MDAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MDAGG +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % construct : List S -> % +--R copy : % -> % dictionary : List S -> % +--R dictionary : () -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extract! : % -> S insert! : (S,%) -> % +--R inspect : % -> S map : ((S -> S),%) -> % +--R removeDuplicates! : % -> % sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R duplicates : % -> List Record(entry: S,count: NonNegativeInteger) +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R hash : % -> SingleInteger if S has SETCAT +--R insert! : (S,%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MultiDictionary examples +==================================================================== + +See Also: +o )show MultiDictionary + +@ {\bf See:} \pageto{MultisetAggregate}{MSETAGG} @@ -20089,6 +24398,46 @@ digraph pic { \pagehead{OrderedAbelianMonoid}{OAMON} \pagepic{ps/v102orderedabelianmonoid.ps}{OAMON}{1.00} +<>= +)set break resume +)sys rm -f OrderedAbelianMonoid.output +)spool OrderedAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedAbelianMonoid +--R OrderedAbelianMonoid is a category constructor +--R Abbreviation for OrderedAbelianMonoid is OAMON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OAMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedAbelianMonoid examples +==================================================================== + +See Also: +o )show OrderedAbelianMonoid + +@ {\bf See:} \pageto{OrderedCancellationAbelianMonoid}{OCAMON} @@ -20202,6 +24551,56 @@ digraph pic { \pagehead{PermutationCategory}{PERMCAT} \pagepic{ps/v102permutationcategory.ps}{PERMCAT}{0.65} +<>= +)set break resume +)sys rm -f PermutationCategory.output +)spool PermutationCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PermutationCategory +--R PermutationCategory S: SetCategory is a category constructor +--R Abbreviation for PermutationCategory is PERMCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PERMCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % +--R ? Boolean ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R commutator : (%,%) -> % conjugate : (%,%) -> % +--R cycle : List S -> % cycles : List List S -> % +--R ?.? : (%,S) -> S eval : (%,S) -> S +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String one? : % -> Boolean +--R orbit : (%,S) -> Set S recip : % -> Union(%,"failed") +--R sample : () -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?<=? : (%,%) -> Boolean if S has ORDSET or S has FINITE +--R ?>? : (%,%) -> Boolean if S has ORDSET or S has FINITE +--R ?>=? : (%,%) -> Boolean if S has ORDSET or S has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R max : (%,%) -> % if S has ORDSET or S has FINITE +--R min : (%,%) -> % if S has ORDSET or S has FINITE +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PermutationCategory examples +==================================================================== + +See Also: +o )show PermutationCategory + +@ {\bf See:} \pagefrom{Group}{GROUP} @@ -20400,6 +24799,118 @@ digraph pic { \pagehead{StreamAggregate}{STAGG} \pagepic{ps/v102streamaggregate.ps}{STAGG}{0.60} +<>= +)set break resume +)sys rm -f StreamAggregate.output +)spool StreamAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show StreamAggregate +--R StreamAggregate S: Type is a category constructor +--R Abbreviation for StreamAggregate is STAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for STAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % concat : (%,S) -> % +--R concat : List % -> % concat : (S,%) -> % +--R concat : (%,%) -> % construct : List S -> % +--R copy : % -> % cycleEntry : % -> % +--R cycleTail : % -> % cyclic? : % -> Boolean +--R delete : (%,Integer) -> % distance : (%,%) -> Integer +--R elt : (%,Integer,S) -> S ?.? : (%,Integer) -> S +--R ?.last : (%,last) -> S ?.rest : (%,rest) -> % +--R ?.first : (%,first) -> S ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R explicitlyFinite? : % -> Boolean first : % -> S +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % +--R last : % -> S leaf? : % -> Boolean +--R leaves : % -> List S map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R nodes : % -> List % possiblyInfinite? : % -> Boolean +--R qelt : (%,Integer) -> S rest : % -> % +--R sample : () -> % second : % -> S +--R tail : % -> % third : % -> S +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R concat! : (%,S) -> % if $ has shallowlyMutable +--R concat! : (%,%) -> % if $ has shallowlyMutable +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R rest : (%,NonNegativeInteger) -> % +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +StreamAggregate examples +==================================================================== + +See Also: +o )show StreamAggregate + +@ {\bf See:} \pageto{LazyStreamAggregate}{LZSTAGG} @@ -20798,6 +25309,108 @@ digraph pic { \pagehead{TriangularSetCategory}{TSETCAT} \pagepic{ps/v102triangularsetcategory.ps}{TSETCAT}{0.35} +<>= +)set break resume +)sys rm -f TriangularSetCategory.output +)spool TriangularSetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TriangularSetCategory +--R TriangularSetCategory(R: IntegralDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for TriangularSetCategory is TSETCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for TSETCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List V coerce : % -> List P +--R coerce : % -> OutputForm collect : (%,V) -> % +--R collectQuasiMonic : % -> % collectUnder : (%,V) -> % +--R collectUpper : (%,V) -> % construct : List P -> % +--R copy : % -> % degree : % -> NonNegativeInteger +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List P last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P +--R removeZero : (P,%) -> P rest : % -> Union(%,"failed") +--R retract : List P -> % sample : () -> % +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R trivialIdeal? : % -> Boolean variables : % -> List V +--R zeroSetSplit : List P -> List % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean +--R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R quasiComponent : % -> Record(close: List P,open: List P) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,V) -> Union(P,"failed") +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R stronglyReduced? : (P,%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TriangularSetCategory examples +==================================================================== + +See Also: +o )show TriangularSetCategory + +@ {\bf See:} \pageto{RegularTriangularSetCategory}{RSETCAT} @@ -21612,6 +26225,53 @@ digraph pic { \pagehead{FiniteDivisorCategory}{FDIVCAT} \pagepic{ps/v102finitedivisorcategory.ps}{FDIVCAT}{0.75} +<>= +)set break resume +)sys rm -f FiniteDivisorCategory.output +)spool FiniteDivisorCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteDivisorCategory +--R FiniteDivisorCategory(F: Field,UP: UnivariatePolynomialCategory t#1,UPUP: UnivariatePolynomialCategory Fraction t#2,R: FunctionFieldCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for FiniteDivisorCategory is FDIVCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FDIVCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % +--R divisor : (F,F) -> % divisor : R -> % +--R hash : % -> SingleInteger latex : % -> String +--R principal? : % -> Boolean reduce : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R decompose : % -> Record(id: FractionalIdeal(UP,Fraction UP,UPUP,R),principalPart: R) +--R divisor : FractionalIdeal(UP,Fraction UP,UPUP,R) -> % +--R generator : % -> Union(R,"failed") +--R ideal : % -> FractionalIdeal(UP,Fraction UP,UPUP,R) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteDivisorCategory examples +==================================================================== + +See Also: +o )show FiniteDivisorCategory + +@ {\bf See:} \pagefrom{AbelianGroup}{ABELGRP} @@ -21787,6 +26447,89 @@ digraph pic { \pagehead{FiniteSetAggregate}{FSAGG} \pagepic{ps/v102finitesetaggregate.ps}{FSAGG}{0.75} +<>= +)set break resume +)sys rm -f FiniteSetAggregate.output +)spool FiniteSetAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteSetAggregate +--R FiniteSetAggregate S: SetCategory is a category constructor +--R Abbreviation for FiniteSetAggregate is FSAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FSAGG +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R bag : List S -> % brace : () -> % +--R brace : List S -> % coerce : % -> OutputForm +--R construct : List S -> % copy : % -> % +--R dictionary : List S -> % dictionary : () -> % +--R difference : (%,%) -> % difference : (%,S) -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R hash : % -> SingleInteger insert! : (S,%) -> % +--R inspect : % -> S intersect : (%,%) -> % +--R latex : % -> String map : ((S -> S),%) -> % +--R max : % -> S if S has ORDSET min : % -> S if S has ORDSET +--R sample : () -> % set : () -> % +--R set : List S -> % subset? : (%,%) -> Boolean +--R union : (%,%) -> % union : (%,S) -> % +--R union : (S,%) -> % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R cardinality : % -> NonNegativeInteger +--R complement : % -> % if S has FINITE +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R index : PositiveInteger -> % if S has FINITE +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R random : () -> % if S has FINITE +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R symmetricDifference : (%,%) -> % +--R universe : () -> % if S has FINITE +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteSetAggregate examples +==================================================================== + +See Also: +o )show FiniteSetAggregate + +@ {\bf See:} \pagefrom{Dictionary}{DIAGG} @@ -22116,6 +26859,83 @@ digraph pic { \pagehead{KeyedDictionary}{KDAGG} \pagepic{ps/v102keyeddictionary.ps}{KDAGG}{1.00} +<>= +)set break resume +)sys rm -f KeyedDictionary.output +)spool KeyedDictionary.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show KeyedDictionary +--R KeyedDictionary(Key: SetCategory,Entry: SetCategory) is a category constructor +--R Abbreviation for KeyedDictionary is KDAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for KDAGG +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean key? : (Key,%) -> Boolean +--R keys : % -> List Key sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List Record(key: Key,entry: Entry) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT +--R construct : List Record(key: Key,entry: Entry) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List Record(key: Key,entry: Entry) -> % +--R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +KeyedDictionary examples +==================================================================== + +See Also: +o )show KeyedDictionary + +@ {\bf See:} \pageto{TableAggregate}{TBAGG} @@ -22360,6 +27180,122 @@ digraph pic { \pagehead{LazyStreamAggregate}{LZSTAGG} \pagepic{ps/v102lazystreamaggregate.ps}{LZSTAGG}{0.65} +<>= +)set break resume +)sys rm -f LazyStreamAggregate.output +)spool LazyStreamAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LazyStreamAggregate +--R LazyStreamAggregate S: Type is a category constructor +--R Abbreviation for LazyStreamAggregate is LZSTAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LZSTAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % complete : % -> % +--R concat : (%,S) -> % concat : List % -> % +--R concat : (S,%) -> % concat : (%,%) -> % +--R construct : List S -> % copy : % -> % +--R cycleEntry : % -> % cycleTail : % -> % +--R cyclic? : % -> Boolean delete : (%,Integer) -> % +--R distance : (%,%) -> Integer elt : (%,Integer,S) -> S +--R ?.? : (%,Integer) -> S ?.last : (%,last) -> S +--R ?.rest : (%,rest) -> % ?.first : (%,first) -> S +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean explicitEntries? : % -> Boolean +--R explicitlyEmpty? : % -> Boolean explicitlyFinite? : % -> Boolean +--R extend : (%,Integer) -> % first : % -> S +--R frst : % -> S index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (S,%,Integer) -> % +--R insert : (%,%,Integer) -> % last : % -> S +--R lazy? : % -> Boolean lazyEvaluate : % -> % +--R leaf? : % -> Boolean leaves : % -> List S +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R new : (NonNegativeInteger,S) -> % nodes : % -> List % +--R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S +--R remove : ((S -> Boolean),%) -> % rest : % -> % +--R rst : % -> % sample : () -> % +--R second : % -> S select : ((S -> Boolean),%) -> % +--R tail : % -> % third : % -> S +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R concat! : (%,S) -> % if $ has shallowlyMutable +--R concat! : (%,%) -> % if $ has shallowlyMutable +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R numberOfComputedEntries : % -> NonNegativeInteger +--R parts : % -> List S if $ has finiteAggregate +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R rest : (%,NonNegativeInteger) -> % +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LazyStreamAggregate examples +==================================================================== + +See Also: +o )show LazyStreamAggregate + +@ {\bf See:} \pagefrom{StreamAggregate}{STAGG} @@ -23182,6 +28118,46 @@ digraph pic { \pagehead{LeftModule}{LMODULE} \pagepic{ps/v102leftmodule.ps}{LMODULE}{0.90} +<>= +)set break resume +)sys rm -f LeftModule.output +)spool LeftModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LeftModule +--R LeftModule R: Rng is a category constructor +--R Abbreviation for LeftModule is LMODULE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LMODULE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LeftModule examples +==================================================================== + +See Also: +o )show LeftModule + +@ {\bf See:} \pageto{BiModule}{BMODULE} @@ -23306,6 +28282,145 @@ digraph pic { \pagehead{ListAggregate}{LSAGG} \pagepic{ps/v102listaggregate.ps}{LSAGG}{0.60} +<>= +)set break resume +)sys rm -f ListAggregate.output +)spool ListAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ListAggregate +--R ListAggregate S: Type is a category constructor +--R Abbreviation for ListAggregate is LSAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LSAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % concat : (%,S) -> % +--R concat : List % -> % concat : (S,%) -> % +--R concat : (%,%) -> % concat! : (%,S) -> % +--R concat! : (%,%) -> % construct : List S -> % +--R copy : % -> % cycleEntry : % -> % +--R cycleTail : % -> % cyclic? : % -> Boolean +--R delete : (%,Integer) -> % delete! : (%,Integer) -> % +--R distance : (%,%) -> Integer elt : (%,Integer,S) -> S +--R ?.? : (%,Integer) -> S ?.last : (%,last) -> S +--R ?.rest : (%,rest) -> % ?.first : (%,first) -> S +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean +--R first : % -> S index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (S,%,Integer) -> % +--R insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> % +--R insert! : (%,%,Integer) -> % last : % -> S +--R leaf? : % -> Boolean leaves : % -> List S +--R list : S -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R nodes : % -> List % possiblyInfinite? : % -> Boolean +--R qelt : (%,Integer) -> S rest : % -> % +--R reverse : % -> % sample : () -> % +--R second : % -> S tail : % -> % +--R third : % -> S value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment Integer) -> % +--R delete! : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R merge : (((S,S) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if S has ORDSET +--R merge! : (((S,S) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R position : ((S -> Boolean),%) -> Integer +--R position : (S,%) -> Integer if S has SETCAT +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % +--R remove! : (S,%) -> % if S has SETCAT +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates! : % -> % if S has SETCAT +--R rest : (%,NonNegativeInteger) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (((S,S) -> Boolean),%) -> % +--R sort : % -> % if S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if S has ORDSET and $ has shallowlyMutable +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if S has ORDSET +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ListAggregate examples +==================================================================== + +See Also: +o )show ListAggregate + +@ {\bf See:} \pageto{AssociationListAggregate}{ALAGG} @@ -23883,6 +28998,84 @@ digraph pic { \pagehead{MultisetAggregate}{MSETAGG} \pagepic{ps/v102multisetaggregate.ps}{MSETAGG}{0.80} +<>= +)set break resume +)sys rm -f MultisetAggregate.output +)spool MultisetAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MultisetAggregate +--R MultisetAggregate S: SetCategory is a category constructor +--R Abbreviation for MultisetAggregate is MSETAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MSETAGG +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R bag : List S -> % brace : () -> % +--R brace : List S -> % coerce : % -> OutputForm +--R construct : List S -> % copy : % -> % +--R dictionary : List S -> % dictionary : () -> % +--R difference : (%,%) -> % difference : (%,S) -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R hash : % -> SingleInteger insert! : (S,%) -> % +--R inspect : % -> S intersect : (%,%) -> % +--R latex : % -> String map : ((S -> S),%) -> % +--R removeDuplicates! : % -> % sample : () -> % +--R set : () -> % set : List S -> % +--R subset? : (%,%) -> Boolean union : (%,%) -> % +--R union : (%,S) -> % union : (S,%) -> % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R duplicates : % -> List Record(entry: S,count: NonNegativeInteger) +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R insert! : (S,%,NonNegativeInteger) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R symmetricDifference : (%,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MultisetAggregate examples +==================================================================== + +See Also: +o )show MultisetAggregate + +@ {\bf See:} \pageto{OrderedMultisetAggregate}{OMSAGG} @@ -24099,6 +29292,50 @@ digraph pic { \pagehead{NonAssociativeRng}{NARNG} \pagepic{ps/v102nonassociativerng.ps}{NARNG}{1.00} +<>= +)set break resume +)sys rm -f NonAssociativeRng.output +)spool NonAssociativeRng.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NonAssociativeRng +--R NonAssociativeRng is a category constructor +--R Abbreviation for NonAssociativeRng is NARNG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for NARNG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antiCommutator : (%,%) -> % +--R associator : (%,%,%) -> % coerce : % -> OutputForm +--R commutator : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R leftPower : (%,PositiveInteger) -> % +--R rightPower : (%,PositiveInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NonAssociativeRng examples +==================================================================== + +See Also: +o )show NonAssociativeRng + +@ {\bf See:} \pageto{NonAssociativeAlgebra}{NAALG} @@ -24252,6 +29489,109 @@ digraph pic { \pagehead{OneDimensionalArrayAggregate}{A1AGG} \pagepic{ps/v102onedimensionalarrayaggregate.ps}{A1AGG}{1.00} +<>= +)set break resume +)sys rm -f OneDimensionalArrayAggregate.output +)spool OneDimensionalArrayAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OneDimensionalArrayAggregate +--R OneDimensionalArrayAggregate S: Type is a category constructor +--R Abbreviation for OneDimensionalArrayAggregate is A1AGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for A1AGG +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S reverse : % -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R merge : (%,%) -> % if S has ORDSET +--R merge : (((S,S) -> Boolean),%,%) -> % +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R position : (S,%) -> Integer if S has SETCAT +--R position : ((S -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if S has ORDSET +--R sort : (((S,S) -> Boolean),%) -> % +--R sort! : % -> % if S has ORDSET and $ has shallowlyMutable +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OneDimensionalArrayAggregate examples +==================================================================== + +See Also: +o )show OneDimensionalArrayAggregate + +@ {\bf See:} \pageto{BitAggregate}{BTAGG} @@ -24750,6 +30090,47 @@ digraph pic { \pagehead{OrderedCancellationAbelianMonoid}{OCAMON} \pagepic{ps/v102orderedcancellationabelianmonoid.ps}{OCAMON}{0.75} +<>= +)set break resume +)sys rm -f OrderedCancellationAbelianMonoid.output +)spool OrderedCancellationAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedCancellationAbelianMonoid +--R OrderedCancellationAbelianMonoid is a category constructor +--R Abbreviation for OrderedCancellationAbelianMonoid is OCAMON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OCAMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedCancellationAbelianMonoid examples +==================================================================== + +See Also: +o )show OrderedCancellationAbelianMonoid + +@ {\bf See:} \pageto{OrderedAbelianGroup}{OAGROUP} @@ -24874,6 +30255,129 @@ digraph pic { \pagehead{RegularTriangularSetCategory}{RSETCAT} \pagepic{ps/v102regulartriangularsetcategory.ps}{RSETCAT}{0.35} +<>= +)set break resume +)sys rm -f RegularTriangularSetCategory.output +)spool RegularTriangularSetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RegularTriangularSetCategory +--R RegularTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for RegularTriangularSetCategory is RSETCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RSETCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List V augment : (List P,%) -> List % +--R augment : (P,List %) -> List % augment : (P,%) -> List % +--R coerce : % -> List P coerce : % -> OutputForm +--R collect : (%,V) -> % collectQuasiMonic : % -> % +--R collectUnder : (%,V) -> % collectUpper : (%,V) -> % +--R construct : List P -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extend : (List P,%) -> List % extend : (P,List %) -> List % +--R extend : (P,%) -> List % extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List P internalAugment : (P,%) -> % +--R intersect : (P,List %) -> List % intersect : (List P,%) -> List % +--R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean +--R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P +--R rest : % -> Union(%,"failed") retract : List P -> % +--R sample : () -> % stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R variables : % -> List V zeroSetSplit : List P -> List % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraicCoefficients? : (P,%) -> Boolean +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List P,List %) -> List % +--R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean +--R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List P,List %) -> List % +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R internalAugment : (List P,%) -> % +--R intersect : (List P,List %) -> List % +--R invertible? : (P,%) -> List Record(val: Boolean,tower: %) +--R invertibleElseSplit? : (P,%) -> Union(Boolean,List %) +--R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %) +--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R purelyAlgebraic? : (P,%) -> Boolean +--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean +--R purelyTranscendental? : (P,%) -> Boolean +--R quasiComponent : % -> Record(close: List P,open: List P) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,V) -> Union(P,"failed") +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (P,%) -> List Record(val: P,tower: %) +--R stronglyReduced? : (P,%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplit : (List P,Boolean) -> List % +--R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RegularTriangularSetCategory examples +==================================================================== + +See Also: +o )show RegularTriangularSetCategory + +@ {\bf See:} \pageto{NormalizedTriangularSetCategory}{NTSCAT} @@ -25534,6 +31038,46 @@ digraph pic { \pagehead{RightModule}{RMODULE} \pagepic{ps/v102rightmodule.ps}{RMODULE}{1.00} +<>= +)set break resume +)sys rm -f RightModule.output +)spool RightModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RightModule +--R RightModule R: Rng is a category constructor +--R Abbreviation for RightModule is RMODULE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RMODULE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RightModule examples +==================================================================== + +See Also: +o )show RightModule + +@ {\bf See:} \pageto{BiModule}{BMODULE} @@ -25651,6 +31195,48 @@ digraph pic { Rng is a Ring that does not necessarily have a unit. +<>= +)set break resume +)sys rm -f Rng.output +)spool Rng.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Rng +--R Rng is a category constructor +--R Abbreviation for Rng is RNG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RNG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Rng examples +==================================================================== + +See Also: +o )show Rng + +@ + {\bf See:} \pageto{Ring}{RING} @@ -25780,6 +31366,47 @@ digraph pic { \pagehead{BiModule}{BMODULE} \pagepic{ps/v102bimodule.ps}{BMODULE}{1.00} +<>= +)set break resume +)sys rm -f BiModule.output +)spool BiModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BiModule +--R BiModule(R: Ring,S: Ring) is a category constructor +--R Abbreviation for BiModule is BMODULE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BMODULE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BiModule examples +==================================================================== + +See Also: +o )show BiModule + +@ {\bf See:} \pageto{AbelianMonoidRing}{AMR} @@ -25933,6 +31560,111 @@ digraph pic { \pagehead{BitAggregate}{BTAGG} \pagepic{ps/v102bitaggregate.ps}{BTAGG}{0.65} +<>= +)set break resume +)sys rm -f BitAggregate.output +)spool BitAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BitAggregate +--R BitAggregate is a category constructor +--R Abbreviation for BitAggregate is BTAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BTAGG +--R +--R------------------------------- Operations -------------------------------- +--R ?/\? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R ?\/? : (%,%) -> % ^? : % -> % +--R ?and? : (%,%) -> % coerce : % -> OutputForm +--R concat : (%,Boolean) -> % concat : (Boolean,%) -> % +--R concat : (%,%) -> % concat : List % -> % +--R construct : List Boolean -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> Boolean +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % nand : (%,%) -> % +--R nor : (%,%) -> % not? : % -> % +--R ?or? : (%,%) -> % qelt : (%,Integer) -> Boolean +--R reverse : % -> % sample : () -> % +--R xor : (%,%) -> % ~? : % -> % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if Boolean has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : ((Boolean -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Boolean,%) -> NonNegativeInteger if Boolean has SETCAT and $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R elt : (%,Integer,Boolean) -> Boolean +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R eval : (%,List Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,List Boolean,List Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R every? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Boolean) -> % if $ has shallowlyMutable +--R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed") +--R first : % -> Boolean if Integer has ORDSET +--R insert : (Boolean,%,Integer) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : ((Boolean -> Boolean),%) -> % +--R map : (((Boolean,Boolean) -> Boolean),%,%) -> % +--R map! : ((Boolean -> Boolean),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Boolean,%) -> Boolean if Boolean has SETCAT and $ has finiteAggregate +--R members : % -> List Boolean if $ has finiteAggregate +--R merge : (((Boolean,Boolean) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if Boolean has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Boolean) -> % +--R parts : % -> List Boolean if $ has finiteAggregate +--R position : ((Boolean -> Boolean),%) -> Integer +--R position : (Boolean,%) -> Integer if Boolean has SETCAT +--R position : (Boolean,%,Integer) -> Integer if Boolean has SETCAT +--R qsetelt! : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R reduce : (((Boolean,Boolean) -> Boolean),%,Boolean,Boolean) -> Boolean if Boolean has SETCAT and $ has finiteAggregate +--R reduce : (((Boolean,Boolean) -> Boolean),%,Boolean) -> Boolean if $ has finiteAggregate +--R reduce : (((Boolean,Boolean) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R remove : (Boolean,%) -> % if Boolean has SETCAT and $ has finiteAggregate +--R remove : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if Boolean has SETCAT and $ has finiteAggregate +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (((Boolean,Boolean) -> Boolean),%) -> % +--R sort : % -> % if Boolean has ORDSET +--R sort! : (((Boolean,Boolean) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if Boolean has ORDSET and $ has shallowlyMutable +--R sorted? : (((Boolean,Boolean) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if Boolean has ORDSET +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BitAggregate examples +==================================================================== + +See Also: +o )show BitAggregate + +@ {\bf See:} \pagefrom{Logic}{LOGIC} @@ -26289,6 +32021,58 @@ digraph pic { \pagehead{NonAssociativeRing}{NASRING} \pagepic{ps/v102nonassociativering.ps}{NASRING}{1.00} +<>= +)set break resume +)sys rm -f NonAssociativeRing.output +)spool NonAssociativeRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NonAssociativeRing +--R NonAssociativeRing is a category constructor +--R Abbreviation for NonAssociativeRing is NASRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for NASRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R antiCommutator : (%,%) -> % associator : (%,%,%) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R commutator : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R leftPower : (%,NonNegativeInteger) -> % +--R leftPower : (%,PositiveInteger) -> % +--R leftRecip : % -> Union(%,"failed") +--R rightPower : (%,NonNegativeInteger) -> % +--R rightPower : (%,PositiveInteger) -> % +--R rightRecip : % -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NonAssociativeRing examples +==================================================================== + +See Also: +o )show NonAssociativeRing + +@ {\bf See:} \pagefrom{MonadWithUnit}{MONADWU} @@ -26460,6 +32244,129 @@ digraph pic { \pagehead{NormalizedTriangularSetCategory}{NTSCAT} \pagepic{ps/v102normalizedtriangularsetcategory.ps}{NTSCAT}{0.45} +<>= +)set break resume +)sys rm -f NormalizedTriangularSetCategory.output +)spool NormalizedTriangularSetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NormalizedTriangularSetCategory +--R NormalizedTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for NormalizedTriangularSetCategory is NTSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for NTSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List V augment : (List P,%) -> List % +--R augment : (P,List %) -> List % augment : (P,%) -> List % +--R coerce : % -> List P coerce : % -> OutputForm +--R collect : (%,V) -> % collectQuasiMonic : % -> % +--R collectUnder : (%,V) -> % collectUpper : (%,V) -> % +--R construct : List P -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extend : (List P,%) -> List % extend : (P,List %) -> List % +--R extend : (P,%) -> List % extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List P internalAugment : (P,%) -> % +--R intersect : (P,List %) -> List % intersect : (List P,%) -> List % +--R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean +--R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P +--R rest : % -> Union(%,"failed") retract : List P -> % +--R sample : () -> % stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R variables : % -> List V zeroSetSplit : List P -> List % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraicCoefficients? : (P,%) -> Boolean +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List P,List %) -> List % +--R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean +--R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List P,List %) -> List % +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R internalAugment : (List P,%) -> % +--R intersect : (List P,List %) -> List % +--R invertible? : (P,%) -> List Record(val: Boolean,tower: %) +--R invertibleElseSplit? : (P,%) -> Union(Boolean,List %) +--R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %) +--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R purelyAlgebraic? : (P,%) -> Boolean +--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean +--R purelyTranscendental? : (P,%) -> Boolean +--R quasiComponent : % -> Record(close: List P,open: List P) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,V) -> Union(P,"failed") +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (P,%) -> List Record(val: P,tower: %) +--R stronglyReduced? : (P,%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplit : (List P,Boolean) -> List % +--R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NormalizedTriangularSetCategory examples +==================================================================== + +See Also: +o )show NormalizedTriangularSetCategory + +@ {\bf See:} \pageto{SquareFreeNormalizedTriangularSetCategory}{SNTSCAT} @@ -26812,6 +32719,49 @@ digraph pic { \pagehead{OrderedAbelianGroup}{OAGROUP} \pagepic{ps/v102orderedabeliangroup.ps}{OAGROUP}{1.00} +<>= +)set break resume +)sys rm -f OrderedAbelianGroup.output +)spool OrderedAbelianGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedAbelianGroup +--R OrderedAbelianGroup is a category constructor +--R Abbreviation for OrderedAbelianGroup is OAGROUP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OAGROUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedAbelianGroup examples +==================================================================== + +See Also: +o )show OrderedAbelianGroup + +@ {\bf See:} \pageto{OrderedRing}{ORDRING} @@ -26932,6 +32882,48 @@ digraph pic { \pagehead{OrderedAbelianMonoidSup}{OAMONS} \pagepic{ps/v102orderedabelianmonoidsup.ps}{OAMONS}{0.80} +<>= +)set break resume +)sys rm -f OrderedAbelianMonoidSup.output +)spool OrderedAbelianMonoidSup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedAbelianMonoidSup +--R OrderedAbelianMonoidSup is a category constructor +--R Abbreviation for OrderedAbelianMonoidSup is OAMONS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OAMONS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % sample : () -> % +--R sup : (%,%) -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedAbelianMonoidSup examples +==================================================================== + +See Also: +o )show OrderedAbelianMonoidSup + +@ {\bf See:} \pagefrom{DirectProductCategory}{DIRPCAT} @@ -27068,6 +33060,86 @@ digraph pic { \pagehead{OrderedMultisetAggregate}{OMSAGG} \pagepic{ps/v102orderedmultisetaggregate.ps}{OMSAGG}{0.50} +<>= +)set break resume +)sys rm -f OrderedMultisetAggregate.output +)spool OrderedMultisetAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedMultisetAggregate +--R OrderedMultisetAggregate S: OrderedSet is a category constructor +--R Abbreviation for OrderedMultisetAggregate is OMSAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OMSAGG +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R bag : List S -> % brace : () -> % +--R brace : List S -> % coerce : % -> OutputForm +--R construct : List S -> % copy : % -> % +--R dictionary : List S -> % dictionary : () -> % +--R difference : (%,%) -> % difference : (%,S) -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R hash : % -> SingleInteger insert! : (S,%) -> % +--R inspect : % -> S intersect : (%,%) -> % +--R latex : % -> String map : ((S -> S),%) -> % +--R max : % -> S merge : (%,%) -> % +--R merge! : (%,%) -> % min : % -> S +--R removeDuplicates! : % -> % sample : () -> % +--R set : () -> % set : List S -> % +--R subset? : (%,%) -> Boolean union : (%,%) -> % +--R union : (%,S) -> % union : (S,%) -> % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R duplicates : % -> List Record(entry: S,count: NonNegativeInteger) +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R insert! : (S,%,NonNegativeInteger) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R symmetricDifference : (%,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedMultisetAggregate examples +==================================================================== + +See Also: +o )show OrderedMultisetAggregate + +@ {\bf See:} \pagefrom{MultisetAggregate}{MSETAGG} @@ -27323,6 +33395,52 @@ digraph pic { \pagehead{Ring}{RING} \pagepic{ps/v102ring.ps}{RING}{1.00} +<>= +)set break resume +)sys rm -f Ring.output +)spool Ring.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Ring +--R Ring is a category constructor +--R Abbreviation for Ring is RING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Ring examples +==================================================================== + +See Also: +o )show Ring + +@ {\bf See:} \pageto{Algebra}{ALGEBRA} @@ -27512,6 +33630,129 @@ digraph pic { \pagehead{SquareFreeRegularTriangularSetCategory}{SFRTCAT} \pagepic{ps/v102squarefreeregulartriangularsetcategory.ps}{SFRTCAT}{0.50} +<>= +)set break resume +)sys rm -f SquareFreeRegularTriangularSetCategory.output +)spool SquareFreeRegularTriangularSetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SquareFreeRegularTriangularSetCategory +--R SquareFreeRegularTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for SquareFreeRegularTriangularSetCategory is SFRTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SFRTCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List V augment : (List P,%) -> List % +--R augment : (P,List %) -> List % augment : (P,%) -> List % +--R coerce : % -> List P coerce : % -> OutputForm +--R collect : (%,V) -> % collectQuasiMonic : % -> % +--R collectUnder : (%,V) -> % collectUpper : (%,V) -> % +--R construct : List P -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extend : (List P,%) -> List % extend : (P,List %) -> List % +--R extend : (P,%) -> List % extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List P internalAugment : (P,%) -> % +--R intersect : (P,List %) -> List % intersect : (List P,%) -> List % +--R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean +--R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P +--R rest : % -> Union(%,"failed") retract : List P -> % +--R sample : () -> % stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R variables : % -> List V zeroSetSplit : List P -> List % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraicCoefficients? : (P,%) -> Boolean +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List P,List %) -> List % +--R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean +--R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List P,List %) -> List % +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R internalAugment : (List P,%) -> % +--R intersect : (List P,List %) -> List % +--R invertible? : (P,%) -> List Record(val: Boolean,tower: %) +--R invertibleElseSplit? : (P,%) -> Union(Boolean,List %) +--R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %) +--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R purelyAlgebraic? : (P,%) -> Boolean +--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean +--R purelyTranscendental? : (P,%) -> Boolean +--R quasiComponent : % -> Record(close: List P,open: List P) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,V) -> Union(P,"failed") +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (P,%) -> List Record(val: P,tower: %) +--R stronglyReduced? : (P,%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplit : (List P,Boolean) -> List % +--R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SquareFreeRegularTriangularSetCategory examples +==================================================================== + +See Also: +o )show SquareFreeRegularTriangularSetCategory + +@ {\bf See:} \pageto{SquareFreeNormalizedTriangularSetCategory}{SNTSCAT} @@ -27859,6 +34100,127 @@ digraph pic { \pagehead{StringAggregate}{SRAGG} \pagepic{ps/v102stringaggregate.ps}{SRAGG}{1.00} +<>= +)set break resume +)sys rm -f StringAggregate.output +)spool StringAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show StringAggregate +--R StringAggregate is a category constructor +--R Abbreviation for StringAggregate is SRAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SRAGG +--R +--R------------------------------- Operations -------------------------------- +--R coerce : Character -> % concat : List % -> % +--R concat : (%,%) -> % concat : (Character,%) -> % +--R concat : (%,Character) -> % construct : List Character -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Character eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (%,%,Integer) -> % leftTrim : (%,Character) -> % +--R lowerCase : % -> % lowerCase! : % -> % +--R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character +--R reverse : % -> % rightTrim : (%,Character) -> % +--R sample : () -> % split : (%,Character) -> List % +--R suffix? : (%,%) -> Boolean trim : (%,CharacterClass) -> % +--R trim : (%,Character) -> % upperCase : % -> % +--R upperCase! : % -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if Character has ORDSET +--R ?<=? : (%,%) -> Boolean if Character has ORDSET +--R ?=? : (%,%) -> Boolean if Character has SETCAT +--R ?>? : (%,%) -> Boolean if Character has ORDSET +--R ?>=? : (%,%) -> Boolean if Character has ORDSET +--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if Character has SETCAT +--R convert : % -> InputForm if Character has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (Character,%) -> NonNegativeInteger if Character has SETCAT and $ has finiteAggregate +--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R elt : (%,Integer,Character) -> Character +--R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R eval : (%,List Character,List Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,Character,Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,List Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Character) -> % if $ has shallowlyMutable +--R find : ((Character -> Boolean),%) -> Union(Character,"failed") +--R first : % -> Character if Integer has ORDSET +--R hash : % -> SingleInteger if Character has SETCAT +--R insert : (Character,%,Integer) -> % +--R latex : % -> String if Character has SETCAT +--R leftTrim : (%,CharacterClass) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Character,Character) -> Character),%,%) -> % +--R map : ((Character -> Character),%) -> % +--R map! : ((Character -> Character),%) -> % if $ has shallowlyMutable +--R match : (%,%,Character) -> NonNegativeInteger +--R match? : (%,%,Character) -> Boolean +--R max : (%,%) -> % if Character has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Character,%) -> Boolean if Character has SETCAT and $ has finiteAggregate +--R members : % -> List Character if $ has finiteAggregate +--R merge : (%,%) -> % if Character has ORDSET +--R merge : (((Character,Character) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Character has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Character) -> % +--R parts : % -> List Character if $ has finiteAggregate +--R position : (CharacterClass,%,Integer) -> Integer +--R position : (%,%,Integer) -> Integer +--R position : (Character,%,Integer) -> Integer if Character has SETCAT +--R position : (Character,%) -> Integer if Character has SETCAT +--R position : ((Character -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R reduce : (((Character,Character) -> Character),%) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character,Character) -> Character if Character has SETCAT and $ has finiteAggregate +--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Character,%) -> % if Character has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if Character has SETCAT and $ has finiteAggregate +--R replace : (%,UniversalSegment Integer,%) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R rightTrim : (%,CharacterClass) -> % +--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,Character) -> Character if $ has shallowlyMutable +--R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if Character has ORDSET +--R sort : (((Character,Character) -> Boolean),%) -> % +--R sort! : % -> % if Character has ORDSET and $ has shallowlyMutable +--R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Character has ORDSET +--R sorted? : (((Character,Character) -> Boolean),%) -> Boolean +--R split : (%,CharacterClass) -> List % +--R substring? : (%,%,Integer) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if Character has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +StringAggregate examples +==================================================================== + +See Also: +o )show StringAggregate + +@ {\bf See:} \pageto{StringCategory}{STRICAT} @@ -28273,6 +34635,109 @@ digraph pic { \pagehead{TableAggregate}{TBAGG} \pagepic{ps/v102tableaggregate.ps}{TBAGG}{0.60} +<>= +)set break resume +)sys rm -f TableAggregate.output +)spool TableAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TableAggregate +--R TableAggregate(Key: SetCategory,Entry: SetCategory) is a category constructor +--R Abbreviation for TableAggregate is TBAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for TBAGG +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Entry eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List Key +--R key? : (Key,%) -> Boolean keys : % -> List Key +--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry +--R sample : () -> % setelt : (%,Key,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List Record(key: Key,entry: Entry) -> % +--R coerce : % -> OutputForm if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R construct : List Record(key: Key,entry: Entry) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if Entry has SETCAT and $ has finiteAggregate +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List Record(key: Key,entry: Entry) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Entry,%) -> Boolean if Entry has SETCAT and $ has finiteAggregate +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R members : % -> List Entry if $ has finiteAggregate +--R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Entry if $ has finiteAggregate +--R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List Record(key: Key,entry: Entry) -> % +--R ?~=? : (%,%) -> Boolean if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TableAggregate examples +==================================================================== + +See Also: +o )show TableAggregate + +@ {\bf See:} \pageto{AssociationListAggregate}{ALAGG} @@ -28722,6 +35187,120 @@ digraph pic { \pagehead{VectorCategory}{VECTCAT} \pagepic{ps/v102vectorcategory.ps}{VECTCAT}{1.00} +<>= +)set break resume +)sys rm -f VectorCategory.output +)spool VectorCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show VectorCategory +--R VectorCategory R: Type is a category constructor +--R Abbreviation for VectorCategory is VECTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for VECTCAT +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP concat : List % -> % +--R concat : (%,%) -> % concat : (R,%) -> % +--R concat : (%,R) -> % construct : List R -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List R eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R new : (NonNegativeInteger,R) -> % qelt : (%,Integer) -> R +--R reverse : % -> % sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (%,R) -> % if R has MONOID +--R ?*? : (R,%) -> % if R has MONOID +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R convert : % -> InputForm if R has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cross : (%,%) -> % if R has RING +--R delete : (%,UniversalSegment Integer) -> % +--R dot : (%,%) -> R if R has RING +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R find : ((R -> Boolean),%) -> Union(R,"failed") +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R length : % -> R if R has RING and R has RADCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R magnitude : % -> R if R has RING and R has RADCAT +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if R has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate +--R members : % -> List R if $ has finiteAggregate +--R merge : (%,%) -> % if R has ORDSET +--R merge : (((R,R) -> Boolean),%,%) -> % +--R min : (%,%) -> % if R has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R outerProduct : (%,%) -> Matrix R if R has RING +--R parts : % -> List R if $ has finiteAggregate +--R position : (R,%,Integer) -> Integer if R has SETCAT +--R position : (R,%) -> Integer if R has SETCAT +--R position : ((R -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R reduce : (((R,R) -> R),%) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R,R) -> R if R has SETCAT and $ has finiteAggregate +--R remove : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (R,%) -> % if R has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if R has SETCAT and $ has finiteAggregate +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % +--R sort! : % -> % if R has ORDSET and $ has shallowlyMutable +--R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if R has ORDSET +--R sorted? : (((R,R) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R zero : NonNegativeInteger -> % if R has ABELMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +VectorCategory examples +==================================================================== + +See Also: +o )show VectorCategory + +@ {\bf See:} \pageto{PointCategory}{PTCAT} @@ -29065,6 +35644,216 @@ digraph pic { \pagehead{AssociationListAggregate}{ALAGG} \pagepic{ps/v102associationlistaggregate.ps}{ALAGG}{0.45} +<>= +)set break resume +)sys rm -f AssociationListAggregate.output +)spool AssociationListAggregate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AssociationListAggregate +--R AssociationListAggregate(Key: SetCategory,Entry: SetCategory) is a category constructor +--R Abbreviation for AssociationListAggregate is ALAGG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ALAGG +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % concat : (%,%) -> % +--R concat : List % -> % concat! : (%,%) -> % +--R copy : % -> % cycleEntry : % -> % +--R cycleTail : % -> % cyclic? : % -> Boolean +--R delete : (%,Integer) -> % delete! : (%,Integer) -> % +--R dictionary : () -> % distance : (%,%) -> Integer +--R ?.rest : (%,rest) -> % elt : (%,Key,Entry) -> Entry +--R ?.? : (%,Key) -> Entry empty : () -> % +--R empty? : % -> Boolean entries : % -> List Entry +--R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean +--R index? : (Integer,%) -> Boolean index? : (Key,%) -> Boolean +--R indices : % -> List Integer indices : % -> List Key +--R insert : (%,%,Integer) -> % insert! : (%,%,Integer) -> % +--R key? : (Key,%) -> Boolean keys : % -> List Key +--R leaf? : % -> Boolean map : ((Entry -> Entry),%) -> % +--R nodes : % -> List % possiblyInfinite? : % -> Boolean +--R qelt : (%,Key) -> Entry rest : % -> % +--R reverse : % -> % sample : () -> % +--R setelt : (%,Key,Entry) -> Entry table : () -> % +--R tail : % -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if Record(key: Key,entry: Entry) has ORDSET +--R ?<=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R ?>? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R ?>=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R assoc : (Key,%) -> Union(Record(key: Key,entry: Entry),"failed") +--R bag : List Record(key: Key,entry: Entry) -> % +--R child? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R concat : (Record(key: Key,entry: Entry),%) -> % +--R concat : (%,Record(key: Key,entry: Entry)) -> % +--R concat! : (%,Record(key: Key,entry: Entry)) -> % +--R construct : List Record(key: Key,entry: Entry) -> % +--R construct : List Record(key: Key,entry: Entry) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM or Record(key: Key,entry: Entry) has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if Entry has SETCAT and $ has finiteAggregate +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment Integer) -> % +--R delete! : (%,UniversalSegment Integer) -> % +--R dictionary : List Record(key: Key,entry: Entry) -> % +--R ?.value : (%,value) -> Record(key: Key,entry: Entry) +--R ?.first : (%,first) -> Record(key: Key,entry: Entry) +--R ?.last : (%,last) -> Record(key: Key,entry: Entry) +--R ?.? : (%,UniversalSegment Integer) -> % +--R ?.? : (%,Integer) -> Record(key: Key,entry: Entry) +--R elt : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) +--R entries : % -> List Record(key: Key,entry: Entry) +--R entry? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Record(key: Key,entry: Entry)) -> % if $ has shallowlyMutable +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Record(key: Key,entry: Entry) +--R first : (%,NonNegativeInteger) -> % +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R insert : (Record(key: Key,entry: Entry),%,Integer) -> % +--R insert! : (Record(key: Key,entry: Entry),%,Integer) -> % +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R last : % -> Record(key: Key,entry: Entry) +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R leaves : % -> List Record(key: Key,entry: Entry) +--R less? : (%,NonNegativeInteger) -> Boolean +--R list : Record(key: Key,entry: Entry) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,%) -> % +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R member? : (Entry,%) -> Boolean if Entry has SETCAT and $ has finiteAggregate +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R members : % -> List Entry if $ has finiteAggregate +--R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R merge : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R merge : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R merge! : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Record(key: Key,entry: Entry)) -> % +--R node? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT +--R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R parts : % -> List Entry if $ has finiteAggregate +--R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R position : (Record(key: Key,entry: Entry),%,Integer) -> Integer if Record(key: Key,entry: Entry) has SETCAT +--R position : (Record(key: Key,entry: Entry),%) -> Integer if Record(key: Key,entry: Entry) has SETCAT +--R position : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Integer +--R qelt : (%,Integer) -> Record(key: Key,entry: Entry) +--R qsetelt! : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if Record(key: Key,entry: Entry) has SETCAT +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate or Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate +--R removeDuplicates! : % -> % if Record(key: Key,entry: Entry) has SETCAT +--R rest : (%,NonNegativeInteger) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R search : (Key,%) -> Union(Entry,"failed") +--R second : % -> Record(key: Key,entry: Entry) +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,value,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,first,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,last,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setfirst! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setlast! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if Record(key: Key,entry: Entry) has ORDSET +--R sort : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%) -> % +--R sort! : % -> % if Record(key: Key,entry: Entry) has ORDSET and $ has shallowlyMutable +--R sort! : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R sorted? : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%) -> Boolean +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List Record(key: Key,entry: Entry) -> % +--R third : % -> Record(key: Key,entry: Entry) +--R value : % -> Record(key: Key,entry: Entry) +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AssociationListAggregate examples +==================================================================== + +See Also: +o )show AssociationListAggregate + +@ {\bf See:} \pagefrom{ListAggregate}{LSAGG} @@ -29581,6 +36370,53 @@ digraph pic { \pagehead{CharacteristicNonZero}{CHARNZ} \pagepic{ps/v102characteristicnonzero.ps}{CHARNZ}{0.90} +<>= +)set break resume +)sys rm -f CharacteristicNonZero.output +)spool CharacteristicNonZero.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CharacteristicNonZero +--R CharacteristicNonZero is a category constructor +--R Abbreviation for CharacteristicNonZero is CHARNZ +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CHARNZ +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CharacteristicNonZero examples +==================================================================== + +See Also: +o )show CharacteristicNonZero + +@ {\bf See:} \pageto{FieldOfPrimeCharacteristic}{FPC} @@ -29734,6 +36570,52 @@ digraph pic { \pagehead{CharacteristicZero}{CHARZ} \pagepic{ps/v102characteristiczero.ps}{CHARZ}{0.90} +<>= +)set break resume +)sys rm -f CharacteristicZero.output +)spool CharacteristicZero.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CharacteristicZero +--R CharacteristicZero is a category constructor +--R Abbreviation for CharacteristicZero is CHARZ +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CHARZ +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CharacteristicZero examples +==================================================================== + +See Also: +o )show CharacteristicZero + +@ {\bf See:} \pageto{FiniteRankAlgebra}{FINRALG} @@ -29881,6 +36763,52 @@ digraph pic { \pagehead{CommutativeRing}{COMRING} \pagepic{ps/v102commutativering.ps}{COMRING}{0.65} +<>= +)set break resume +)sys rm -f CommutativeRing.output +)spool CommutativeRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show CommutativeRing +--R CommutativeRing is a category constructor +--R Abbreviation for CommutativeRing is COMRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for COMRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +CommutativeRing examples +==================================================================== + +See Also: +o )show CommutativeRing + +@ Commutative Rings are a subset of IntegralDomains. \pageto{IntegralDomain}{INTDOM}. @@ -30055,6 +36983,55 @@ digraph pic { \pagehead{DifferentialRing}{DIFRING} \pagepic{ps/v102differentialring.ps}{DIFRING}{0.90} +<>= +)set break resume +)sys rm -f DifferentialRing.output +)spool DifferentialRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DifferentialRing +--R DifferentialRing is a category constructor +--R Abbreviation for DifferentialRing is DIFRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIFRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,NonNegativeInteger) -> % D : % -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm differentiate : % -> % +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DifferentialRing examples +==================================================================== + +See Also: +o )show DifferentialRing + +@ {\bf See:} \pageto{IntegerNumberSystem}{INS} @@ -30235,6 +37212,52 @@ digraph pic { \pagehead{EntireRing}{ENTIRER} \pagepic{ps/v102EntireRing.ps}{ENTIRER}{0.65} +<>= +)set break resume +)sys rm -f EntireRing.output +)spool EntireRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show EntireRing +--R EntireRing is a category constructor +--R Abbreviation for EntireRing is ENTIRER +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ENTIRER +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +EntireRing examples +==================================================================== + +See Also: +o )show EntireRing + +@ {\bf See:} \pageto{DivisionRing}{DIVRING} @@ -30400,6 +37423,57 @@ digraph pic { \pagehead{FreeModuleCat}{FMCAT} \pagepic{ps/v102freemodulecat.ps}{FMCAT}{0.75} +<>= +)set break resume +)sys rm -f FreeModuleCat.output +)spool FreeModuleCat.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeModuleCat +--R FreeModuleCat(R: Ring,Basis: SetCategory) is a category constructor +--R Abbreviation for FreeModuleCat is FMCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FMCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,Basis) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coefficient : (%,Basis) -> R coefficients : % -> List R +--R coerce : Basis -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R leadingMonomial : % -> Basis +--R map : ((R -> R),%) -> % monom : (Basis,R) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R reductum : % -> % retract : % -> Basis +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R leadingTerm : % -> Record(k: Basis,c: R) +--R listOfTerms : % -> List Record(k: Basis,c: R) +--R numberOfMonomials : % -> NonNegativeInteger +--R retractIfCan : % -> Union(Basis,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeModuleCat examples +==================================================================== + +See Also: +o )show FreeModuleCat + +@ {\bf See:} \pagefrom{BiModule}{BMODULE} @@ -30618,6 +37692,53 @@ digraph pic { \pagehead{LeftAlgebra}{LALG} \pagepic{ps/v102leftalgebra.ps}{LALG}{1.00} +<>= +)set break resume +)sys rm -f LeftAlgebra.output +)spool LeftAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LeftAlgebra +--R LeftAlgebra R: Ring is a category constructor +--R Abbreviation for LeftAlgebra is LALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LeftAlgebra examples +==================================================================== + +See Also: +o )show LeftAlgebra + +@ {\bf See:} \pagefrom{LeftModule}{LMODULE} @@ -30760,6 +37881,54 @@ digraph pic { \pagehead{LinearlyExplicitRingOver}{LINEXP} \pagepic{ps/v102linearlyexplicitringover.ps}{LINEXP}{0.90} +<>= +)set break resume +)sys rm -f LinearlyExplicitRingOver.output +)spool LinearlyExplicitRingOver.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LinearlyExplicitRingOver +--R LinearlyExplicitRingOver R: Ring is a category constructor +--R Abbreviation for LinearlyExplicitRingOver is LINEXP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LINEXP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : Matrix % -> Matrix R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LinearlyExplicitRingOver examples +==================================================================== + +See Also: +o )show LinearlyExplicitRingOver + +@ {\bf See:} \pageto{FullyLinearlyExplicitRingOver}{FLINEXP} @@ -30925,6 +38094,47 @@ digraph pic { \pagehead{Module}{MODULE} \pagepic{ps/v102module.ps}{MODULE}{1.00} +<>= +)set break resume +)sys rm -f Module.output +)spool Module.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Module +--R Module R: CommutativeRing is a category constructor +--R Abbreviation for Module is MODULE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MODULE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Module examples +==================================================================== + +See Also: +o )show Module + +@ {\bf See:} \pageto{Algebra}{ALGEBRA} @@ -31064,6 +38274,57 @@ digraph pic { \pagehead{OrderedRing}{ORDRING} \pagepic{ps/v102orderedring.ps}{ORDRING}{0.75} +<>= +)set break resume +)sys rm -f OrderedRing.output +)spool OrderedRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedRing +--R OrderedRing is a category constructor +--R Abbreviation for OrderedRing is ORDRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ORDRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R negative? : % -> Boolean one? : % -> Boolean +--R positive? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % sign : % -> Integer +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedRing examples +==================================================================== + +See Also: +o )show OrderedRing + +@ {\bf See:} \pageto{DirectProductCategory}{DIRPCAT} @@ -31270,6 +38531,58 @@ digraph pic { \pagehead{PartialDifferentialRing}{PDRING} \pagepic{ps/v102partialdifferentialring.ps}{PDRING}{1.00} +<>= +)set break resume +)sys rm -f PartialDifferentialRing.output +)spool PartialDifferentialRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PartialDifferentialRing +--R PartialDifferentialRing S: SetCategory is a category constructor +--R Abbreviation for PartialDifferentialRing is PDRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PDRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List S) -> % D : (%,S) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm differentiate : (%,List S) -> % +--R differentiate : (%,S) -> % hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,List S,List NonNegativeInteger) -> % +--R D : (%,S,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R differentiate : (%,List S,List NonNegativeInteger) -> % +--R differentiate : (%,S,NonNegativeInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PartialDifferentialRing examples +==================================================================== + +See Also: +o )show PartialDifferentialRing + +@ {\bf See:} \pageto{DifferentialExtension}{DIFEXT} @@ -31490,6 +38803,122 @@ digraph pic { \pagehead{PointCategory}{PTCAT} \pagepic{ps/v102pointcategory.ps}{PTCAT}{1.00} +<>= +)set break resume +)sys rm -f PointCategory.output +)spool PointCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PointCategory +--R PointCategory R: Ring is a category constructor +--R Abbreviation for PointCategory is PTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PTCAT +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP concat : List % -> % +--R concat : (%,%) -> % concat : (R,%) -> % +--R concat : (%,R) -> % construct : List R -> % +--R convert : List R -> % copy : % -> % +--R cross : (%,%) -> % delete : (%,Integer) -> % +--R dimension : % -> PositiveInteger ?.? : (%,Integer) -> R +--R elt : (%,Integer,R) -> R empty : () -> % +--R empty? : % -> Boolean entries : % -> List R +--R eq? : (%,%) -> Boolean extend : (%,List R) -> % +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R new : (NonNegativeInteger,R) -> % point : List R -> % +--R qelt : (%,Integer) -> R reverse : % -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (%,R) -> % if R has MONOID +--R ?*? : (R,%) -> % if R has MONOID +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R convert : % -> InputForm if R has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R dot : (%,%) -> R if R has RING +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R find : ((R -> Boolean),%) -> Union(R,"failed") +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R length : % -> R if R has RING and R has RADCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R magnitude : % -> R if R has RING and R has RADCAT +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if R has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate +--R members : % -> List R if $ has finiteAggregate +--R merge : (%,%) -> % if R has ORDSET +--R merge : (((R,R) -> Boolean),%,%) -> % +--R min : (%,%) -> % if R has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R outerProduct : (%,%) -> Matrix R if R has RING +--R parts : % -> List R if $ has finiteAggregate +--R position : (R,%,Integer) -> Integer if R has SETCAT +--R position : (R,%) -> Integer if R has SETCAT +--R position : ((R -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R reduce : (((R,R) -> R),%) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R,R) -> R if R has SETCAT and $ has finiteAggregate +--R remove : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (R,%) -> % if R has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if R has SETCAT and $ has finiteAggregate +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % +--R sort! : % -> % if R has ORDSET and $ has shallowlyMutable +--R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if R has ORDSET +--R sorted? : (((R,R) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R zero : NonNegativeInteger -> % if R has ABELMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PointCategory examples +==================================================================== + +See Also: +o )show PointCategory + +@ {\bf See:} \pagefrom{VectorCategory}{VECTCAT} @@ -31789,6 +39218,82 @@ parameters of RectangularMatrixCategory do not satisfy FiniteLinearAggregate(R) as required in MatrixCategory. The RectangularMatrix domain is matrices of fixed dimension. + +<>= +)set break resume +)sys rm -f RectangularMatrixCategory.output +)spool RectangularMatrixCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RectangularMatrixCategory +--R RectangularMatrixCategory(m: NonNegativeInteger,n: NonNegativeInteger,R: Ring,Row: DirectProductCategory(t#2,t#3),Col: DirectProductCategory(t#1,t#3)) is a category constructor +--R Abbreviation for RectangularMatrixCategory is RMATCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RMATCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antisymmetric? : % -> Boolean +--R coerce : % -> OutputForm column : (%,Integer) -> Col +--R copy : % -> % diagonal? : % -> Boolean +--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R latex : % -> String listOfLists : % -> List List R +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R matrix : List List R -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger qelt : (%,Integer,Integer) -> R +--R row : (%,Integer) -> Row sample : () -> % +--R square? : % -> Boolean symmetric? : % -> Boolean +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (NonNegativeInteger,%) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate +--R members : % -> List R if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R nullSpace : % -> List Col if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R parts : % -> List R if $ has finiteAggregate +--R rank : % -> NonNegativeInteger if R has INTDOM +--R rowEchelon : % -> % if R has EUCDOM +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RectangularMatrixCategory examples +==================================================================== + +See Also: +o )show RectangularMatrixCategory + +@ + {\bf See:} \pageto{SquareMatrixCategory}{SMATCAT} @@ -32161,6 +39666,129 @@ digraph pic { \pagehead{SquareFreeNormalizedTriangularSetCategory}{SNTSCAT} \pagepic{ps/v102squarefreenormalizedtriangularsetcategory.ps}{SNTSCAT}{0.45} +<>= +)set break resume +)sys rm -f SquareFreeNormalizedTriangularSetCategory.output +)spool SquareFreeNormalizedTriangularSetCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SquareFreeNormalizedTriangularSetCategory +--R SquareFreeNormalizedTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor +--R Abbreviation for SquareFreeNormalizedTriangularSetCategory is SNTSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SNTSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List V augment : (List P,%) -> List % +--R augment : (P,List %) -> List % augment : (P,%) -> List % +--R coerce : % -> List P coerce : % -> OutputForm +--R collect : (%,V) -> % collectQuasiMonic : % -> % +--R collectUnder : (%,V) -> % collectUpper : (%,V) -> % +--R construct : List P -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extend : (List P,%) -> List % extend : (P,List %) -> List % +--R extend : (P,%) -> List % extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List P internalAugment : (P,%) -> % +--R intersect : (P,List %) -> List % intersect : (List P,%) -> List % +--R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean +--R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P +--R rest : % -> Union(%,"failed") retract : List P -> % +--R sample : () -> % stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R variables : % -> List V zeroSetSplit : List P -> List % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraicCoefficients? : (P,%) -> Boolean +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List P,List %) -> List % +--R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean +--R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List P,List %) -> List % +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R internalAugment : (List P,%) -> % +--R intersect : (List P,List %) -> List % +--R invertible? : (P,%) -> List Record(val: Boolean,tower: %) +--R invertibleElseSplit? : (P,%) -> Union(Boolean,List %) +--R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %) +--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R purelyAlgebraic? : (P,%) -> Boolean +--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean +--R purelyTranscendental? : (P,%) -> Boolean +--R quasiComponent : % -> Record(close: List P,open: List P) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,V) -> Union(P,"failed") +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (P,%) -> List Record(val: P,tower: %) +--R stronglyReduced? : (P,%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplit : (List P,Boolean) -> List % +--R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SquareFreeNormalizedTriangularSetCategory examples +==================================================================== + +See Also: +o )show SquareFreeNormalizedTriangularSetCategory + +@ {\bf See:} \pagefrom{NormalizedTriangularSetCategory}{NTSCAT} @@ -32481,6 +40109,128 @@ digraph pic { \pagehead{StringCategory}{STRICAT} \pagepic{ps/v102stringcategory.ps}{STRICAT}{0.75} +<>= +)set break resume +)sys rm -f StringCategory.output +)spool StringCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show StringCategory +--R StringCategory is a category constructor +--R Abbreviation for StringCategory is STRICAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for STRICAT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean OMwrite : (%,Boolean) -> String +--R OMwrite : % -> String coerce : % -> OutputForm +--R coerce : Character -> % concat : List % -> % +--R concat : (%,%) -> % concat : (Character,%) -> % +--R concat : (%,Character) -> % construct : List Character -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Character eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R latex : % -> String leftTrim : (%,Character) -> % +--R lowerCase : % -> % lowerCase! : % -> % +--R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character +--R reverse : % -> % rightTrim : (%,Character) -> % +--R sample : () -> % split : (%,Character) -> List % +--R string : Integer -> % suffix? : (%,%) -> Boolean +--R trim : (%,CharacterClass) -> % trim : (%,Character) -> % +--R upperCase : % -> % upperCase! : % -> % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if Character has ORDSET +--R ?<=? : (%,%) -> Boolean if Character has ORDSET +--R ?>? : (%,%) -> Boolean if Character has ORDSET +--R ?>=? : (%,%) -> Boolean if Character has ORDSET +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if Character has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (Character,%) -> NonNegativeInteger if Character has SETCAT and $ has finiteAggregate +--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R elt : (%,Integer,Character) -> Character +--R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R eval : (%,List Character,List Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,Character,Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,List Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Character) -> % if $ has shallowlyMutable +--R find : ((Character -> Boolean),%) -> Union(Character,"failed") +--R first : % -> Character if Integer has ORDSET +--R insert : (Character,%,Integer) -> % +--R leftTrim : (%,CharacterClass) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Character,Character) -> Character),%,%) -> % +--R map : ((Character -> Character),%) -> % +--R map! : ((Character -> Character),%) -> % if $ has shallowlyMutable +--R match : (%,%,Character) -> NonNegativeInteger +--R match? : (%,%,Character) -> Boolean +--R max : (%,%) -> % if Character has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Character,%) -> Boolean if Character has SETCAT and $ has finiteAggregate +--R members : % -> List Character if $ has finiteAggregate +--R merge : (%,%) -> % if Character has ORDSET +--R merge : (((Character,Character) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Character has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Character) -> % +--R parts : % -> List Character if $ has finiteAggregate +--R position : (CharacterClass,%,Integer) -> Integer +--R position : (%,%,Integer) -> Integer +--R position : (Character,%,Integer) -> Integer if Character has SETCAT +--R position : (Character,%) -> Integer if Character has SETCAT +--R position : ((Character -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R reduce : (((Character,Character) -> Character),%) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character,Character) -> Character if Character has SETCAT and $ has finiteAggregate +--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Character,%) -> % if Character has SETCAT and $ has finiteAggregate +--R removeDuplicates : % -> % if Character has SETCAT and $ has finiteAggregate +--R replace : (%,UniversalSegment Integer,%) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R rightTrim : (%,CharacterClass) -> % +--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,Character) -> Character if $ has shallowlyMutable +--R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if Character has ORDSET +--R sort : (((Character,Character) -> Boolean),%) -> % +--R sort! : % -> % if Character has ORDSET and $ has shallowlyMutable +--R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Character has ORDSET +--R sorted? : (((Character,Character) -> Boolean),%) -> Boolean +--R split : (%,CharacterClass) -> List % +--R substring? : (%,%,Integer) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +StringCategory examples +==================================================================== + +See Also: +o )show StringCategory + +@ {\bf See:} \pagefrom{OpenMath}{OM} @@ -32824,6 +40574,85 @@ digraph pic { \pagehead{UnivariateSkewPolynomialCategory}{OREPCAT} \pagepic{ps/v102univariateskewpolynomialcategory.ps}{OREPCAT}{0.55} +<>= +)set break resume +)sys rm -f UnivariateSkewPolynomialCategory.output +)spool UnivariateSkewPolynomialCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariateSkewPolynomialCategory +--R UnivariateSkewPolynomialCategory R: Ring is a category constructor +--R Abbreviation for UnivariateSkewPolynomialCategory is OREPCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OREPCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % apply : (%,R,R) -> R +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R content : % -> R if R has GCDDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD +--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R leftGcd : (%,%) -> % if R has FIELD +--R leftLcm : (%,%) -> % if R has FIELD +--R leftQuotient : (%,%) -> % if R has FIELD +--R leftRemainder : (%,%) -> % if R has FIELD +--R minimumDegree : % -> NonNegativeInteger +--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R monomial : (R,NonNegativeInteger) -> % +--R primitivePart : % -> % if R has GCDDOM +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R rightExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD +--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R rightGcd : (%,%) -> % if R has FIELD +--R rightLcm : (%,%) -> % if R has FIELD +--R rightQuotient : (%,%) -> % if R has FIELD +--R rightRemainder : (%,%) -> % if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariateSkewPolynomialCategory examples +==================================================================== + +See Also: +o )show UnivariateSkewPolynomialCategory + +@ {\bf See:} \pageto{LinearOrdinaryDifferentialOperatorCategory}{LODOCAT} @@ -33320,6 +41149,54 @@ digraph pic { \pagehead{XAlgebra}{XALG} \pagepic{ps/v102xalgebra.ps}{XALG}{0.70} +<>= +)set break resume +)sys rm -f XAlgebra.output +)spool XAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show XAlgebra +--R XAlgebra R: Ring is a category constructor +--R Abbreviation for XAlgebra is XALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for XALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +XAlgebra examples +==================================================================== + +See Also: +o )show XAlgebra + +@ {\bf See:} \pageto{XFreeAlgebra}{XFALG} @@ -33496,6 +41373,54 @@ digraph pic { \pagehead{Algebra}{ALGEBRA} \pagepic{ps/v102algebra.ps}{ALGEBRA}{0.65} +<>= +)set break resume +)sys rm -f Algebra.output +)spool Algebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Algebra +--R Algebra R: CommutativeRing is a category constructor +--R Abbreviation for Algebra is ALGEBRA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ALGEBRA +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Algebra examples +==================================================================== + +See Also: +o )show Algebra + +@ {\bf See:} \pageto{DivisionRing}{DIVRING} @@ -33708,6 +41633,67 @@ digraph pic { \pagehead{DifferentialExtension}{DIFEXT} \pagepic{ps/v102differentialextension.ps}{DIFEXT}{0.65} +<>= +)set break resume +)sys rm -f DifferentialExtension.output +)spool DifferentialExtension.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DifferentialExtension +--R DifferentialExtension R: Ring is a category constructor +--R Abbreviation for DifferentialExtension is DIFEXT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIFEXT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : % -> % if R has DIFRING D : (%,(R -> R)) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,(R -> R)) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DifferentialExtension examples +==================================================================== + +See Also: +o )show DifferentialExtension + +@ {\bf See:} \pageto{ComplexCategory}{COMPCAT} @@ -33941,6 +41927,56 @@ digraph pic { \pagehead{FullyLinearlyExplicitRingOver}{FLINEXP} \pagepic{ps/v102fullylinearlyexplicitringover.ps}{FLINEXP}{1.00} +<>= +)set break resume +)sys rm -f FullyLinearlyExplicitRingOver.output +)spool FullyLinearlyExplicitRingOver.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FullyLinearlyExplicitRingOver +--R FullyLinearlyExplicitRingOver R: Ring is a category constructor +--R Abbreviation for FullyLinearlyExplicitRingOver is FLINEXP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FLINEXP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : Matrix % -> Matrix R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FullyLinearlyExplicitRingOver examples +==================================================================== + +See Also: +o )show FullyLinearlyExplicitRingOver + +@ {\bf See:} \pageto{ComplexCategory}{COMPCAT} @@ -34132,6 +42168,48 @@ digraph pic { \pagehead{LieAlgebra}{LIECAT} \pagepic{ps/v102liealgebra.ps}{LIECAT}{1.00} +<>= +)set break resume +)sys rm -f LieAlgebra.output +)spool LieAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LieAlgebra +--R LieAlgebra R: CommutativeRing is a category constructor +--R Abbreviation for LieAlgebra is LIECAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LIECAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R construct : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LieAlgebra examples +==================================================================== + +See Also: +o )show LieAlgebra + +@ {\bf See:} \pageto{FreeLieAlgebra}{FLALG} @@ -34281,6 +42359,90 @@ digraph pic { \pagehead{LinearOrdinaryDifferentialOperatorCategory}{LODOCAT} \pagepic{ps/v102linearordinarydifferentialoperatorcategory.ps}{LODOCAT}{0.50} +<>= +)set break resume +)sys rm -f LinearOrdinaryDifferentialOperatorCategory.output +)spool LinearOrdinaryDifferentialOperatorCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LinearOrdinaryDifferentialOperatorCategory +--R LinearOrdinaryDifferentialOperatorCategory A: Ring is a category constructor +--R Abbreviation for LinearOrdinaryDifferentialOperatorCategory is LODOCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LODOCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (A,%) -> % ?*? : (%,A) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : () -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R adjoint : % -> % apply : (%,A,A) -> A +--R coefficients : % -> List A coerce : A -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger ?.? : (%,A) -> A +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A one? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> A sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> A +--R coerce : Fraction Integer -> % if A has RETRACT FRAC INT +--R content : % -> A if A has GCDDOM +--R directSum : (%,%) -> % if A has FIELD +--R exquo : (%,A) -> Union(%,"failed") if A has INTDOM +--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R leftExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R leftGcd : (%,%) -> % if A has FIELD +--R leftLcm : (%,%) -> % if A has FIELD +--R leftQuotient : (%,%) -> % if A has FIELD +--R leftRemainder : (%,%) -> % if A has FIELD +--R minimumDegree : % -> NonNegativeInteger +--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monomial : (A,NonNegativeInteger) -> % +--R primitivePart : % -> % if A has GCDDOM +--R retract : % -> Fraction Integer if A has RETRACT FRAC INT +--R retract : % -> Integer if A has RETRACT INT +--R retractIfCan : % -> Union(A,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if A has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if A has RETRACT INT +--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R rightExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R rightGcd : (%,%) -> % if A has FIELD +--R rightLcm : (%,%) -> % if A has FIELD +--R rightQuotient : (%,%) -> % if A has FIELD +--R rightRemainder : (%,%) -> % if A has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R symmetricPower : (%,NonNegativeInteger) -> % if A has FIELD +--R symmetricProduct : (%,%) -> % if A has FIELD +--R symmetricSquare : % -> % if A has FIELD +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LinearOrdinaryDifferentialOperatorCategory examples +==================================================================== + +See Also: +o )show LinearOrdinaryDifferentialOperatorCategory + +@ {\bf See:} \pagefrom{Eltable}{ELTAB} @@ -34612,6 +42774,52 @@ digraph pic { \pagehead{NonAssociativeAlgebra}{NAALG} \pagepic{ps/v102nonassociativealgebra.ps}{NAALG}{0.75} +<>= +)set break resume +)sys rm -f NonAssociativeAlgebra.output +)spool NonAssociativeAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NonAssociativeAlgebra +--R NonAssociativeAlgebra R: CommutativeRing is a category constructor +--R Abbreviation for NonAssociativeAlgebra is NAALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for NAALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antiCommutator : (%,%) -> % +--R associator : (%,%,%) -> % coerce : % -> OutputForm +--R commutator : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R leftPower : (%,PositiveInteger) -> % +--R plenaryPower : (%,PositiveInteger) -> % +--R rightPower : (%,PositiveInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NonAssociativeAlgebra examples +==================================================================== + +See Also: +o )show NonAssociativeAlgebra + +@ {\bf See:} \pageto{FiniteRankNonAssociativeAlgebra}{FINAALG} @@ -34787,6 +42995,48 @@ digraph pic { \pagehead{VectorSpace}{VSPACE} \pagepic{ps/v102vectorspace.ps}{VSPACE}{1.00} +<>= +)set break resume +)sys rm -f VectorSpace.output +)spool VectorSpace.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show VectorSpace +--R VectorSpace S: Field is a category constructor +--R Abbreviation for VectorSpace is VSPACE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for VSPACE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (S,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,S) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm dimension : () -> CardinalNumber +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +VectorSpace examples +==================================================================== + +See Also: +o )show VectorSpace + +@ {\bf See:} \pageto{ExtensionField}{XF} @@ -34929,6 +43179,72 @@ digraph pic { \pagehead{XFreeAlgebra}{XFALG} \pagepic{ps/v102xfreealgebra.ps}{XFALG}{0.50} +<>= +)set break resume +)sys rm -f XFreeAlgebra.output +)spool XFreeAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show XFreeAlgebra +--R XFreeAlgebra(vl: OrderedSet,R: Ring) is a category constructor +--R Abbreviation for XFreeAlgebra is XFALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for XFALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (vl,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coef : (%,%) -> R coerce : vl -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm constant : % -> R +--R constant? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lquo : (%,%) -> % +--R lquo : (%,vl) -> % map : ((R -> R),%) -> % +--R mirror : % -> % monomial? : % -> Boolean +--R one? : % -> Boolean quasiRegular : % -> % +--R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") +--R rquo : (%,%) -> % rquo : (%,vl) -> % +--R sample : () -> % varList : % -> List vl +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coef : (%,OrderedFreeMonoid vl) -> R +--R coerce : OrderedFreeMonoid vl -> % +--R lquo : (%,OrderedFreeMonoid vl) -> % +--R mindeg : % -> OrderedFreeMonoid vl +--R mindegTerm : % -> Record(k: OrderedFreeMonoid vl,c: R) +--R monom : (OrderedFreeMonoid vl,R) -> % +--R retract : % -> OrderedFreeMonoid vl +--R retractIfCan : % -> Union(OrderedFreeMonoid vl,"failed") +--R rquo : (%,OrderedFreeMonoid vl) -> % +--R sh : (%,NonNegativeInteger) -> % if R has COMRING +--R sh : (%,%) -> % if R has COMRING +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +XFreeAlgebra examples +==================================================================== + +See Also: +o )show XFreeAlgebra + +@ {\bf See:} \pageto{XPolynomialsCat}{XPOLYC} @@ -35250,6 +43566,140 @@ digraph pic { \pagehead{DirectProductCategory}{DIRPCAT} \pagepic{ps/v102directproductcategory.ps}{DIRPCAT}{0.40} +<>= +)set break resume +)sys rm -f DirectProductCategory.output +)spool DirectProductCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DirectProductCategory +--R DirectProductCategory(dim: NonNegativeInteger,R: Type) is a category constructor +--R Abbreviation for DirectProductCategory is DIRPCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIRPCAT +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has RING 1 : () -> % if R has MONOID +--R 0 : () -> % if R has CABMON coerce : % -> Vector R +--R copy : % -> % directProduct : Vector R -> % +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List R eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R map : ((R -> R),%) -> % qelt : (%,Integer) -> R +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (PositiveInteger,%) -> % if R has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if R has CABMON +--R ?*? : (R,%) -> % if R has RING +--R ?*? : (%,R) -> % if R has RING +--R ?*? : (%,%) -> % if R has MONOID +--R ?*? : (Integer,%) -> % if R has RING +--R ?**? : (%,PositiveInteger) -> % if R has MONOID +--R ?**? : (%,NonNegativeInteger) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has RING +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDRING or R has OAMONS +--R ?<=? : (%,%) -> Boolean if R has ORDRING or R has OAMONS +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has ORDRING or R has OAMONS +--R ?>=? : (%,%) -> Boolean if R has ORDRING or R has OAMONS +--R D : (%,(R -> R)) -> % if R has RING +--R D : (%,(R -> R),NonNegativeInteger) -> % if R has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R D : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R D : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R D : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Ring)) +--R D : % -> % if and(has(R,DifferentialRing),has(R,Ring)) +--R ?^? : (%,PositiveInteger) -> % if R has MONOID +--R ?^? : (%,NonNegativeInteger) -> % if R has MONOID +--R abs : % -> % if R has ORDRING +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if R has RING +--R coerce : R -> % if R has SETCAT +--R coerce : Fraction Integer -> % if and(has(R,RetractableTo Fraction Integer),has(R,SetCategory)) +--R coerce : Integer -> % if and(has(R,RetractableTo Integer),has(R,SetCategory)) or R has RING +--R coerce : % -> OutputForm if R has SETCAT +--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : (%,(R -> R)) -> % if R has RING +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R differentiate : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R differentiate : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring)) +--R differentiate : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Ring)) +--R differentiate : % -> % if and(has(R,DifferentialRing),has(R,Ring)) +--R dimension : () -> CardinalNumber if R has FIELD +--R dot : (%,%) -> R if R has RING +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R index : PositiveInteger -> % if R has FINITE +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if R has FINITE +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if R has ORDRING or R has OAMONS +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate +--R members : % -> List R if $ has finiteAggregate +--R min : (%,%) -> % if R has ORDRING or R has OAMONS +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if R has ORDRING +--R one? : % -> Boolean if R has MONOID +--R parts : % -> List R if $ has finiteAggregate +--R positive? : % -> Boolean if R has ORDRING +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R random : () -> % if R has FINITE +--R recip : % -> Union(%,"failed") if R has MONOID +--R reducedSystem : Matrix % -> Matrix R if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring)) +--R reducedSystem : Matrix % -> Matrix Integer if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring)) +--R retract : % -> R if R has SETCAT +--R retract : % -> Fraction Integer if and(has(R,RetractableTo Fraction Integer),has(R,SetCategory)) +--R retract : % -> Integer if and(has(R,RetractableTo Integer),has(R,SetCategory)) +--R retractIfCan : % -> Union(R,"failed") if R has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if and(has(R,RetractableTo Fraction Integer),has(R,SetCategory)) +--R retractIfCan : % -> Union(Integer,"failed") if and(has(R,RetractableTo Integer),has(R,SetCategory)) +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R sign : % -> Integer if R has ORDRING +--R size : () -> NonNegativeInteger if R has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") if R has CABMON +--R sup : (%,%) -> % if R has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if R has RING +--R zero? : % -> Boolean if R has CABMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DirectProductCategory examples +==================================================================== + +See Also: +o )show DirectProductCategory + +@ {\bf See:} \pagefrom{BiModule}{BMODULE} @@ -35732,6 +44182,55 @@ digraph pic { \pagehead{DivisionRing}{DIVRING} \pagepic{ps/v102divisionring.ps}{DIVRING}{0.65} +<>= +)set break resume +)sys rm -f DivisionRing.output +)spool DivisionRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DivisionRing +--R DivisionRing is a category constructor +--R Abbreviation for DivisionRing is DIVRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIVRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Fraction Integer -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DivisionRing examples +==================================================================== + +See Also: +o )show DivisionRing + +@ {\bf See:} \pageto{Field}{FIELD} @@ -35931,6 +44430,86 @@ digraph pic { \pagehead{FiniteRankNonAssociativeAlgebra}{FINAALG} \pagepic{ps/v102finiteranknonassociativealgebra.ps}{FINAALG}{0.80} +<>= +)set break resume +)sys rm -f FiniteRankNonAssociativeAlgebra.output +)spool FiniteRankNonAssociativeAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteRankNonAssociativeAlgebra +--R FiniteRankNonAssociativeAlgebra R: CommutativeRing is a category constructor +--R Abbreviation for FiniteRankNonAssociativeAlgebra is FINAALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FINAALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % alternative? : () -> Boolean +--R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean +--R antiCommutator : (%,%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % coerce : % -> OutputForm +--R commutative? : () -> Boolean commutator : (%,%) -> % +--R flexible? : () -> Boolean hash : % -> SingleInteger +--R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean +--R jordanAlgebra? : () -> Boolean latex : % -> String +--R leftAlternative? : () -> Boolean leftDiscriminant : Vector % -> R +--R leftNorm : % -> R leftTrace : % -> R +--R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean +--R powerAssociative? : () -> Boolean rank : () -> PositiveInteger +--R rightAlternative? : () -> Boolean rightDiscriminant : Vector % -> R +--R rightNorm : % -> R rightTrace : % -> R +--R sample : () -> % someBasis : () -> Vector % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R associatorDependence : () -> List Vector R if R has INTDOM +--R conditionsForIdempotents : Vector % -> List Polynomial R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R leftPower : (%,PositiveInteger) -> % +--R leftRecip : % -> Union(%,"failed") if R has INTDOM +--R leftRegularRepresentation : (%,Vector %) -> Matrix R +--R leftTraceMatrix : Vector % -> Matrix R +--R leftUnit : () -> Union(%,"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R noncommutativeJordanAlgebra? : () -> Boolean +--R plenaryPower : (%,PositiveInteger) -> % +--R recip : % -> Union(%,"failed") if R has INTDOM +--R represents : (Vector R,Vector %) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R rightPower : (%,PositiveInteger) -> % +--R rightRecip : % -> Union(%,"failed") if R has INTDOM +--R rightRegularRepresentation : (%,Vector %) -> Matrix R +--R rightTraceMatrix : Vector % -> Matrix R +--R rightUnit : () -> Union(%,"failed") if R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R structuralConstants : Vector % -> Vector Matrix R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteRankNonAssociativeAlgebra examples +==================================================================== + +See Also: +o )show FiniteRankNonAssociativeAlgebra + +@ {\bf See:} \pageto{FramedNonAssociativeAlgebra}{FRNAALG} @@ -36833,6 +45412,58 @@ digraph pic { \pagehead{FreeLieAlgebra}{FLALG} \pagepic{ps/v102freeliealgebra.ps}{FLALG}{1.00} +<>= +)set break resume +)sys rm -f FreeLieAlgebra.output +)spool FreeLieAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeLieAlgebra +--R FreeLieAlgebra(VarSet: OrderedSet,R: CommutativeRing) is a category constructor +--R Abbreviation for FreeLieAlgebra is FLALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FLALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R LiePoly : LyndonWord VarSet -> % 0 : () -> % +--R coerce : VarSet -> % coerce : % -> OutputForm +--R construct : (%,%) -> % degree : % -> NonNegativeInteger +--R eval : (%,VarSet,%) -> % hash : % -> SingleInteger +--R latex : % -> String mirror : % -> % +--R sample : () -> % varList : % -> List VarSet +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R coef : (XRecursivePolynomial(VarSet,R),%) -> R +--R coerce : % -> XRecursivePolynomial(VarSet,R) +--R coerce : % -> XDistributedPolynomial(VarSet,R) +--R eval : (%,List VarSet,List %) -> % +--R lquo : (XRecursivePolynomial(VarSet,R),%) -> XRecursivePolynomial(VarSet,R) +--R rquo : (XRecursivePolynomial(VarSet,R),%) -> XRecursivePolynomial(VarSet,R) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R trunc : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeLieAlgebra examples +==================================================================== + +See Also: +o )show FreeLieAlgebra + +@ {\bf See:} \pagefrom{LieAlgebra}{LIECAT} @@ -37043,6 +45674,56 @@ digraph pic { \pagehead{IntegralDomain}{INTDOM} \pagepic{ps/v102integraldomain.ps}{INTDOM}{0.65} +<>= +)set break resume +)sys rm -f IntegralDomain.output +)spool IntegralDomain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IntegralDomain +--R IntegralDomain is a category constructor +--R Abbreviation for IntegralDomain is INTDOM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for INTDOM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exquo : (%,%) -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IntegralDomain examples +==================================================================== + +See Also: +o )show IntegralDomain + +@ All Commutative Rings are Integral Domains. \pagefrom{CommutativeRing}{COMRING} Integral Domains are a subset of Unique Factorization domains. @@ -37278,6 +45959,59 @@ digraph pic { \pagehead{MonogenicLinearOperator}{MLO} \pagepic{ps/v102monogeniclinearoperator.ps}{MLO}{0.60} +<>= +)set break resume +)sys rm -f MonogenicLinearOperator.output +)spool MonogenicLinearOperator.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MonogenicLinearOperator +--R MonogenicLinearOperator R: Ring is a category constructor +--R Abbreviation for MonogenicLinearOperator is MLO +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MLO +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R one? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : R -> % if R has COMRING +--R minimumDegree : % -> NonNegativeInteger +--R monomial : (R,NonNegativeInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MonogenicLinearOperator examples +==================================================================== + +See Also: +o )show MonogenicLinearOperator + +@ {\bf See:} \pagefrom{Algebra}{ALGEBRA} @@ -37513,6 +46247,89 @@ digraph pic { \pagehead{OctonionCategory}{OC} \pagepic{ps/v102octonioncategory.ps}{OC}{1.00} +<>= +)set break resume +)sys rm -f OctonionCategory.output +)spool OctonionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OctonionCategory +--R OctonionCategory R: CommutativeRing is a category constructor +--R Abbreviation for OctonionCategory is OC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> R if R has RNS +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R hash : % -> SingleInteger imagE : % -> R +--R imagI : % -> R imagJ : % -> R +--R imagK : % -> R imagi : % -> R +--R imagj : % -> R imagk : % -> R +--R inv : % -> % if R has FIELD latex : % -> String +--R map : ((R -> R),%) -> % norm : % -> R +--R octon : (R,R,R,R,R,R,R,R) -> % one? : % -> Boolean +--R real : % -> R recip : % -> Union(%,"failed") +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R convert : % -> InputForm if R has KONVERT INFORM +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List Equation R) -> % if R has EVALAB R +--R eval : (%,Equation R) -> % if R has EVALAB R +--R eval : (%,R,R) -> % if R has EVALAB R +--R eval : (%,List R,List R) -> % if R has EVALAB R +--R index : PositiveInteger -> % if R has FINITE +--R lookup : % -> PositiveInteger if R has FINITE +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R random : () -> % if R has FINITE +--R rational : % -> Fraction Integer if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R size : () -> NonNegativeInteger if R has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OctonionCategory examples +==================================================================== + +See Also: +o )show OctonionCategory + +@ {\bf See:} \pagefrom{Algebra}{ALGEBRA} @@ -38001,6 +46818,106 @@ digraph pic { \pagehead{QuaternionCategory}{QUATCAT} \pagepic{ps/v102quaternioncategory.ps}{QUATCAT}{0.70} +<>= +)set break resume +)sys rm -f QuaternionCategory.output +)spool QuaternionCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show QuaternionCategory +--R QuaternionCategory R: CommutativeRing is a category constructor +--R Abbreviation for QuaternionCategory is QUATCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for QUATCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> R if R has RNS +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R hash : % -> SingleInteger imagI : % -> R +--R imagJ : % -> R imagK : % -> R +--R inv : % -> % if R has FIELD latex : % -> String +--R map : ((R -> R),%) -> % norm : % -> R +--R one? : % -> Boolean quatern : (R,R,R,R) -> % +--R real : % -> R recip : % -> Union(%,"failed") +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has FIELD +--R ?*? : (%,Fraction Integer) -> % if R has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R ?^? : (%,Integer) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT +--R convert : % -> InputForm if R has KONVERT INFORM +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : % -> % if R has DIFRING +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List Equation R) -> % if R has EVALAB R +--R eval : (%,Equation R) -> % if R has EVALAB R +--R eval : (%,R,R) -> % if R has EVALAB R +--R eval : (%,List R,List R) -> % if R has EVALAB R +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R rational : % -> Fraction Integer if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +QuaternionCategory examples +==================================================================== + +See Also: +o )show QuaternionCategory + +@ {\bf See:} \pagefrom{Algebra}{ALGEBRA} @@ -38469,6 +47386,122 @@ of a given dimension The SquareMatrix domain is for square matrices of fixed dimension. + +<>= +)set break resume +)sys rm -f SquareMatrixCategory.output +)spool SquareMatrixCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SquareMatrixCategory +--R SquareMatrixCategory(ndim: NonNegativeInteger,R: Ring,Row: DirectProductCategory(t#1,t#2),Col: DirectProductCategory(t#1,t#2)) is a category constructor +--R Abbreviation for SquareMatrixCategory is SMATCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SMATCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Row,%) -> Row ?*? : (%,Col) -> Col +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : % -> % if R has DIFRING D : (%,(R -> R)) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % antisymmetric? : % -> Boolean +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm column : (%,Integer) -> Col +--R copy : % -> % diagonal : % -> Row +--R diagonal? : % -> Boolean diagonalMatrix : List R -> % +--R diagonalProduct : % -> R elt : (%,Integer,Integer) -> R +--R elt : (%,Integer,Integer,R) -> R empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger latex : % -> String +--R listOfLists : % -> List List R map : ((R -> R),%) -> % +--R map : (((R,R) -> R),%,%) -> % matrix : List List R -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R one? : % -> Boolean qelt : (%,Integer,Integer) -> R +--R recip : % -> Union(%,"failed") retract : % -> R +--R row : (%,Integer) -> Row sample : () -> % +--R scalarMatrix : R -> % square? : % -> Boolean +--R symmetric? : % -> Boolean trace : % -> R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> R if R has commutative * +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,(R -> R)) -> % +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R inverse : % -> Union(%,"failed") if R has FIELD +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate +--R members : % -> List R if $ has finiteAggregate +--R minordet : % -> R if R has commutative * +--R more? : (%,NonNegativeInteger) -> Boolean +--R nullSpace : % -> List Col if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R parts : % -> List R if $ has finiteAggregate +--R rank : % -> NonNegativeInteger if R has INTDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R rowEchelon : % -> % if R has EUCDOM +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SquareMatrixCategory examples +==================================================================== + +See Also: +o )show SquareMatrixCategory + +@ + {\bf See:} \pagefrom{BiModule}{BMODULE} @@ -38980,6 +48013,75 @@ digraph pic { \pagehead{XPolynomialsCat}{XPOLYC} \pagepic{ps/v102xpolynomialscat.ps}{XPOLYC}{0.50} +<>= +)set break resume +)sys rm -f XPolynomialsCat.output +)spool XPolynomialsCat.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show XPolynomialsCat +--R XPolynomialsCat(vl: OrderedSet,R: Ring) is a category constructor +--R Abbreviation for XPolynomialsCat is XPOLYC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for XPOLYC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (vl,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coef : (%,%) -> R coerce : vl -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm constant : % -> R +--R constant? : % -> Boolean degree : % -> NonNegativeInteger +--R hash : % -> SingleInteger latex : % -> String +--R lquo : (%,%) -> % lquo : (%,vl) -> % +--R map : ((R -> R),%) -> % mirror : % -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R quasiRegular : % -> % quasiRegular? : % -> Boolean +--R recip : % -> Union(%,"failed") rquo : (%,%) -> % +--R rquo : (%,vl) -> % sample : () -> % +--R varList : % -> List vl zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coef : (%,OrderedFreeMonoid vl) -> R +--R coerce : OrderedFreeMonoid vl -> % +--R lquo : (%,OrderedFreeMonoid vl) -> % +--R maxdeg : % -> OrderedFreeMonoid vl +--R mindeg : % -> OrderedFreeMonoid vl +--R mindegTerm : % -> Record(k: OrderedFreeMonoid vl,c: R) +--R monom : (OrderedFreeMonoid vl,R) -> % +--R retract : % -> OrderedFreeMonoid vl +--R retractIfCan : % -> Union(OrderedFreeMonoid vl,"failed") +--R rquo : (%,OrderedFreeMonoid vl) -> % +--R sh : (%,NonNegativeInteger) -> % if R has COMRING +--R sh : (%,%) -> % if R has COMRING +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R trunc : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +XPolynomialsCat examples +==================================================================== + +See Also: +o )show XPolynomialsCat + +@ {\bf See:} \pagefrom{XFreeAlgebra}{XFALG} @@ -39236,6 +48338,69 @@ digraph pic { \pagehead{AbelianMonoidRing}{AMR} \pagepic{ps/v102abelianmonoidring.ps}{AMR}{0.65} +<>= +)set break resume +)sys rm -f AbelianMonoidRing.output +)spool AbelianMonoidRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AbelianMonoidRing +--R AbelianMonoidRing(R: Ring,E: OrderedAbelianMonoid) is a category constructor +--R Abbreviation for AbelianMonoidRing is AMR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for AMR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> E hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R monomial : (R,E) -> % monomial? : % -> Boolean +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : R -> % if R has COMRING +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AbelianMonoidRing examples +==================================================================== + +See Also: +o )show AbelianMonoidRing + +@ {\bf See:} \pageto{FiniteAbelianMonoidRing}{FAMR} @@ -39530,6 +48695,61 @@ digraph pic { \pagehead{FortranMachineTypeCategory}{FMTC} \pagepic{ps/v102fortranmachinetypecategory.ps}{FMTC}{0.40} +<>= +)set break resume +)sys rm -f FortranMachineTypeCategory.output +)spool FortranMachineTypeCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranMachineTypeCategory +--R FortranMachineTypeCategory is a category constructor +--R Abbreviation for FortranMachineTypeCategory is FMTC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FMTC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R retract : % -> Integer sample : () -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exquo : (%,%) -> Union(%,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranMachineTypeCategory examples +==================================================================== + +See Also: +o )show FortranMachineTypeCategory + +@ {\bf See:} \pagefrom{IntegralDomain}{INTDOM} @@ -39750,6 +48970,99 @@ digraph pic { \pagehead{FramedNonAssociativeAlgebra}{FRNAALG} \pagepic{ps/v102framednonassociativealgebra.ps}{FRNAALG}{0.75} +<>= +)set break resume +)sys rm -f FramedNonAssociativeAlgebra.output +)spool FramedNonAssociativeAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FramedNonAssociativeAlgebra +--R FramedNonAssociativeAlgebra R: CommutativeRing is a category constructor +--R Abbreviation for FramedNonAssociativeAlgebra is FRNAALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FRNAALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % alternative? : () -> Boolean +--R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean +--R antiCommutator : (%,%) -> % apply : (Matrix R,%) -> % +--R associative? : () -> Boolean associator : (%,%,%) -> % +--R basis : () -> Vector % coerce : % -> OutputForm +--R commutative? : () -> Boolean commutator : (%,%) -> % +--R convert : Vector R -> % convert : % -> Vector R +--R coordinates : % -> Vector R ?.? : (%,Integer) -> R +--R flexible? : () -> Boolean hash : % -> SingleInteger +--R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean +--R jordanAlgebra? : () -> Boolean latex : % -> String +--R leftAlternative? : () -> Boolean leftDiscriminant : () -> R +--R leftDiscriminant : Vector % -> R leftNorm : % -> R +--R leftTrace : % -> R leftTraceMatrix : () -> Matrix R +--R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean +--R powerAssociative? : () -> Boolean rank : () -> PositiveInteger +--R represents : Vector R -> % rightAlternative? : () -> Boolean +--R rightDiscriminant : () -> R rightDiscriminant : Vector % -> R +--R rightNorm : % -> R rightTrace : % -> R +--R rightTraceMatrix : () -> Matrix R sample : () -> % +--R someBasis : () -> Vector % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R associatorDependence : () -> List Vector R if R has INTDOM +--R conditionsForIdempotents : () -> List Polynomial R +--R conditionsForIdempotents : Vector % -> List Polynomial R +--R coordinates : Vector % -> Matrix R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R leftRecip : % -> Union(%,"failed") if R has INTDOM +--R leftRegularRepresentation : % -> Matrix R +--R leftRegularRepresentation : (%,Vector %) -> Matrix R +--R leftTraceMatrix : Vector % -> Matrix R +--R leftUnit : () -> Union(%,"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R noncommutativeJordanAlgebra? : () -> Boolean +--R plenaryPower : (%,PositiveInteger) -> % +--R recip : % -> Union(%,"failed") if R has INTDOM +--R represents : (Vector R,Vector %) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R rightRecip : % -> Union(%,"failed") if R has INTDOM +--R rightRegularRepresentation : % -> Matrix R +--R rightRegularRepresentation : (%,Vector %) -> Matrix R +--R rightTraceMatrix : Vector % -> Matrix R +--R rightUnit : () -> Union(%,"failed") if R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R structuralConstants : () -> Vector Matrix R +--R structuralConstants : Vector % -> Vector Matrix R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FramedNonAssociativeAlgebra examples +==================================================================== + +See Also: +o )show FramedNonAssociativeAlgebra + +@ {\bf See:} \pagefrom{FiniteRankNonAssociativeAlgebra}{FINAALG} @@ -40346,6 +49659,59 @@ digraph pic { \pagehead{GcdDomain}{GCDDOM} \pagepic{ps/v102gcddomain.ps}{GCDDOM}{0.65} +<>= +)set break resume +)sys rm -f GcdDomain.output +)spool GcdDomain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GcdDomain +--R GcdDomain is a category constructor +--R Abbreviation for GcdDomain is GCDDOM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for GCDDOM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exquo : (%,%) -> Union(%,"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GcdDomain examples +==================================================================== + +See Also: +o )show GcdDomain + +@ {\bf See:} \pageto{IntervalCategory}{INTCAT} @@ -40575,6 +49941,61 @@ digraph pic { \pagehead{OrderedIntegralDomain}{OINTDOM} \pagepic{ps/v102orderedintegraldomain.ps}{OINTDOM}{0.45} +<>= +)set break resume +)sys rm -f OrderedIntegralDomain.output +)spool OrderedIntegralDomain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedIntegralDomain +--R OrderedIntegralDomain is a category constructor +--R Abbreviation for OrderedIntegralDomain is OINTDOM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OINTDOM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R negative? : % -> Boolean one? : % -> Boolean +--R positive? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % sign : % -> Integer +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exquo : (%,%) -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedIntegralDomain examples +==================================================================== + +See Also: +o )show OrderedIntegralDomain + +@ {\bf See:} \pageto{IntegerNumberSystem}{INS} @@ -40771,6 +50192,82 @@ digraph pic { \pagehead{FiniteAbelianMonoidRing}{FAMR} \pagepic{ps/v102finiteabelianmonoidring.ps}{FAMR}{0.40} +<>= +)set break resume +)sys rm -f FiniteAbelianMonoidRing.output +)spool FiniteAbelianMonoidRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteAbelianMonoidRing +--R FiniteAbelianMonoidRing(R: Ring,E: OrderedAbelianMonoid) is a category constructor +--R Abbreviation for FiniteAbelianMonoidRing is FAMR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FAMR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> E ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R mapExponents : ((E -> E),%) -> % minimumDegree : % -> E +--R monomial : (R,E) -> % monomial? : % -> Boolean +--R one? : % -> Boolean pomopo! : (%,R,E,%) -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT +--R coerce : % -> % if R has INTDOM +--R content : % -> R if R has GCDDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R numberOfMonomials : % -> NonNegativeInteger +--R primitivePart : % -> % if R has GCDDOM +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteAbelianMonoidRing examples +==================================================================== + +See Also: +o )show FiniteAbelianMonoidRing + +@ {\bf See:} \pageto{PolynomialCategory}{POLYCAT} @@ -41147,6 +50644,85 @@ digraph pic { \pagehead{IntervalCategory}{INTCAT} \pagepic{ps/v102intervalcategory.ps}{INTCAT}{0.60} +<>= +)set break resume +)sys rm -f IntervalCategory.output +)spool IntervalCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IntervalCategory +--R IntervalCategory R: Join(FloatingPointSystem,TranscendentalFunctionCategory) is a category constructor +--R Abbreviation for IntervalCategory is INTCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for INTCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % +--R ?**? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % acos : % -> % +--R acosh : % -> % acot : % -> % +--R acoth : % -> % acsc : % -> % +--R acsch : % -> % asec : % -> % +--R asech : % -> % asin : % -> % +--R asinh : % -> % associates? : (%,%) -> Boolean +--R atan : % -> % atanh : % -> % +--R coerce : Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R contains? : (%,R) -> Boolean cos : % -> % +--R cosh : % -> % cot : % -> % +--R coth : % -> % csc : % -> % +--R csch : % -> % exp : % -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inf : % -> R +--R interval : Fraction Integer -> % interval : R -> % +--R interval : (R,R) -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R log : % -> % max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R nthRoot : (%,Integer) -> % one? : % -> Boolean +--R pi : () -> % positive? : % -> Boolean +--R qinterval : (R,R) -> % recip : % -> Union(%,"failed") +--R retract : % -> Integer sample : () -> % +--R sec : % -> % sech : % -> % +--R sin : % -> % sinh : % -> % +--R sqrt : % -> % sup : % -> R +--R tan : % -> % tanh : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R width : % -> R zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exquo : (%,%) -> Union(%,"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IntervalCategory examples +==================================================================== + +See Also: +o )show IntervalCategory + +@ {\bf See:} \pagefrom{GcdDomain}{GCDDOM} @@ -41498,6 +51074,72 @@ digraph pic { \pagehead{PowerSeriesCategory}{PSCAT} \pagepic{ps/v102powerseriescategory.ps}{PSCAT}{0.60} +<>= +)set break resume +)sys rm -f PowerSeriesCategory.output +)spool PowerSeriesCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PowerSeriesCategory +--R PowerSeriesCategory(Coef: Ring,Expon: OrderedAbelianMonoid,Var: OrderedSet) is a category constructor +--R Abbreviation for PowerSeriesCategory is PSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,Expon) -> Coef +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> Expon +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial : (%,Var,Expon) -> % +--R monomial : (Coef,Expon) -> % monomial? : % -> Boolean +--R one? : % -> Boolean pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % variables : % -> List Var +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coerce : Coef -> % if Coef has COMRING +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R monomial : (%,List Var,List Expon) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PowerSeriesCategory examples +==================================================================== + +See Also: +o )show PowerSeriesCategory + +@ {\bf See:} \pageto{MultivariateTaylorSeriesCategory}{MTSCAT} @@ -41778,14 +51420,69 @@ digraph pic { \pagehead{PrincipalIdealDomain}{PID} \pagepic{ps/v102principalidealdomain.ps}{PID}{0.65} +<>= +)set break resume +)sys rm -f PrincipalIdealDomain.output +)spool PrincipalIdealDomain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PrincipalIdealDomain +--R PrincipalIdealDomain is a category constructor +--R Abbreviation for PrincipalIdealDomain is PID +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PID +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PrincipalIdealDomain examples +==================================================================== + +See Also: +o )show PrincipalIdealDomain + +@ + +{\bf See:} + Unique Factorization Domains are a subset of Principal Ideal Domains. \pagefrom{UniqueFactorizationDomain}{UFD} Principal Ideal Domains are a subset of Euclidean Domains. \pageto{EuclideanDomain}{EUCDOM} -{\bf See:} - -\pageto{EuclideanDomain}{EUCDOM} \pagefrom{GcdDomain}{GCDDOM} {\bf Exports:}\\ @@ -41975,6 +51672,61 @@ digraph pic { \pagehead{UniqueFactorizationDomain}{UFD} \pagepic{ps/v102uniquefactorizationdomain.ps}{UFD}{0.65} +<>= +)set break resume +)sys rm -f UniqueFactorizationDomain.output +)spool UniqueFactorizationDomain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UniqueFactorizationDomain +--R UniqueFactorizationDomain is a category constructor +--R Abbreviation for UniqueFactorizationDomain is UFD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UFD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exquo : (%,%) -> Union(%,"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UniqueFactorizationDomain examples +==================================================================== + +See Also: +o )show UniqueFactorizationDomain + +@ All Integral Domains are UniqueFactorizationDomains. \pagefrom{IntegralDomain}{INTDOM}. Unique Factorization Domains are a subset of Principal Ideal Domains. @@ -42444,6 +52196,68 @@ digraph pic { \pagehead{EuclideanDomain}{EUCDOM} \pagepic{ps/v102euclideandomain.ps}{EUCDOM}{0.65} +<>= +)set break resume +)sys rm -f EuclideanDomain.output +)spool EuclideanDomain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show EuclideanDomain +--R EuclideanDomain is a category constructor +--R Abbreviation for EuclideanDomain is EUCDOM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for EUCDOM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +EuclideanDomain examples +==================================================================== + +See Also: +o )show EuclideanDomain + +@ Principal Ideal Domains are a subset of Euclidean Domains. \pagefrom{PrincipalIdealDomain}{PID}. Euclidean Domains are a subset of Fields. @@ -42781,6 +52595,125 @@ digraph pic { \pagehead{MultivariateTaylorSeriesCategory}{MTSCAT} \pagepic{ps/v102multivariatetaylorseriescategory.ps}{MTSCAT}{1.00} +<>= +)set break resume +)sys rm -f MultivariateTaylorSeriesCategory.output +)spool MultivariateTaylorSeriesCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MultivariateTaylorSeriesCategory +--R MultivariateTaylorSeriesCategory(Coef: Ring,Var: OrderedSet) is a category constructor +--R Abbreviation for MultivariateTaylorSeriesCategory is MTSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MTSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Coef) -> % ?*? : (Coef,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List Var) -> % D : (%,Var) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R differentiate : (%,Var) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % eval : (%,List Var,List %) -> % +--R eval : (%,Var,%) -> % hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R variables : % -> List Var zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : (%,List Var,List NonNegativeInteger) -> % +--R D : (%,Var,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,List Var,List NonNegativeInteger) -> % +--R coefficient : (%,Var,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents Var) -> Coef +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : % -> % if Coef has INTDOM +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R degree : % -> IndexedExponents Var +--R differentiate : (%,List Var,List NonNegativeInteger) -> % +--R differentiate : (%,Var,NonNegativeInteger) -> % +--R differentiate : (%,List Var) -> % +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,NonNegativeInteger) -> % +--R integrate : (%,Var) -> % if Coef has ALGEBRA FRAC INT +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List Var,List NonNegativeInteger) -> % +--R monomial : (%,Var,NonNegativeInteger) -> % +--R monomial : (Coef,IndexedExponents Var) -> % +--R monomial : (%,Var,IndexedExponents Var) -> % +--R monomial : (%,List Var,List IndexedExponents Var) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,Var,NonNegativeInteger) -> NonNegativeInteger +--R order : (%,Var) -> NonNegativeInteger +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef +--R polynomial : (%,NonNegativeInteger) -> Polynomial Coef +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MultivariateTaylorSeriesCategory examples +==================================================================== + +See Also: +o )show MultivariateTaylorSeriesCategory + +@ {\bf See:} \pagefrom{Evalable}{EVALAB} @@ -43135,6 +53068,67 @@ digraph pic { \pagehead{PolynomialFactorizationExplicit}{PFECAT} \pagepic{ps/v102polynomialfactorizationexplicit.ps}{PFECAT}{0.80} +<>= +)set break resume +)sys rm -f PolynomialFactorizationExplicit.output +)spool PolynomialFactorizationExplicit.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PolynomialFactorizationExplicit +--R PolynomialFactorizationExplicit is a category constructor +--R Abbreviation for PolynomialFactorizationExplicit is PFECAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PFECAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ +--R exquo : (%,%) -> Union(%,"failed") +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PolynomialFactorizationExplicit examples +==================================================================== + +See Also: +o )show PolynomialFactorizationExplicit + +@ {\bf See:} \pageto{PolynomialCategory}{POLYCAT} @@ -43410,6 +53404,94 @@ digraph pic { \pagehead{UnivariatePowerSeriesCategory}{UPSCAT} \pagepic{ps/v102univariatepowerseriescategory.ps}{UPSCAT}{0.55} +<>= +)set break resume +)sys rm -f UnivariatePowerSeriesCategory.output +)spool UnivariatePowerSeriesCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariatePowerSeriesCategory +--R UnivariatePowerSeriesCategory(Coef: Ring,Expon: OrderedAbelianMonoid) is a category constructor +--R Abbreviation for UnivariatePowerSeriesCategory is UPSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficient : (%,Expon) -> Coef coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Expon ?.? : (%,Expon) -> Coef +--R extend : (%,Expon) -> % hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial : (Coef,Expon) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : (%,Expon) -> Expon +--R order : % -> Expon pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % truncate : (%,Expon,Expon) -> % +--R truncate : (%,Expon) -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Expon,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Expon,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R ?^? : (%,NonNegativeInteger) -> % +--R approximate : (%,Expon) -> Coef if Coef has **: (Coef,Expon) -> Coef and Coef has coerce: Symbol -> Coef +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coerce : Coef -> % if Coef has COMRING +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R differentiate : % -> % if Coef has *: (Expon,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Expon,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef +--R ?.? : (%,%) -> % if Expon has SGROUP +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Expon) -> Coef +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R monomial : (%,List SingletonAsOrderedSet,List Expon) -> % +--R monomial : (%,SingletonAsOrderedSet,Expon) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> Stream Record(k: Expon,c: Coef) +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariatePowerSeriesCategory examples +==================================================================== + +See Also: +o )show UnivariatePowerSeriesCategory + +@ {\bf See:} \pageto{LocalPowerSeriesCategory}{LOCPOWC} @@ -43819,6 +53901,73 @@ digraph pic { \pagehead{Field}{FIELD} \pagepic{ps/v102field.ps}{FIELD}{1.00} +<>= +)set break resume +)sys rm -f Field.output +)spool Field.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Field +--R Field is a category constructor +--R Abbreviation for Field is FIELD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FIELD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Field examples +==================================================================== + +See Also: +o )show Field + +@ Euclidean Domains are a subset of Fields. \pagefrom{EuclideanDomain}{EUCDOM} \pageto{PseudoAlgebraicClosureOfPerfectFieldCategory}{PACPERC} @@ -44077,6 +54226,100 @@ digraph pic { \pagehead{IntegerNumberSystem}{INS} \pagepic{ps/v102integernumbersystem.ps}{INS}{0.30} +<>= +)set break resume +)sys rm -f IntegerNumberSystem.output +)spool IntegerNumberSystem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IntegerNumberSystem +--R IntegerNumberSystem is a category constructor +--R Abbreviation for IntegerNumberSystem is INS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for INS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R addmod : (%,%,%) -> % associates? : (%,%) -> Boolean +--R base : () -> % binomial : (%,%) -> % +--R bit? : (%,%) -> Boolean coerce : Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> DoubleFloat +--R convert : % -> Float convert : % -> Pattern Integer +--R convert : % -> InputForm convert : % -> Integer +--R copy : % -> % dec : % -> % +--R differentiate : % -> % even? : % -> Boolean +--R factor : % -> Factored % factorial : % -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> % hash : % -> SingleInteger +--R inc : % -> % init : () -> % +--R invmod : (%,%) -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R length : % -> % mask : % -> % +--R max : (%,%) -> % min : (%,%) -> % +--R mulmod : (%,%,%) -> % negative? : % -> Boolean +--R odd? : % -> Boolean one? : % -> Boolean +--R permutation : (%,%) -> % positive? : % -> Boolean +--R positiveRemainder : (%,%) -> % powmod : (%,%,%) -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R random : % -> % random : () -> % +--R rational : % -> Fraction Integer rational? : % -> Boolean +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Integer sample : () -> % +--R shift : (%,%) -> % sign : % -> Integer +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % submod : (%,%,%) -> % +--R symmetricRemainder : (%,%) -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R rationalIfCan : % -> Union(Fraction Integer,"failed") +--R reducedSystem : Matrix % -> Matrix Integer +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IntegerNumberSystem examples +==================================================================== + +See Also: +o )show IntegerNumberSystem + +@ {\bf See:} \pagefrom{CharacteristicZero}{CHARZ} @@ -44593,6 +54836,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{LocalPowerSeriesCategory}{LOCPOWC} \pagepic{ps/v102localpowerseriescategory.ps}{LOCPOWC}{0.70} + <>= )set break resume )sys rm -f LocalPowerSeriesCategory.output @@ -45057,11 +55301,78 @@ digraph pic { @ - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{PAdicIntegerCategory}{PADICCT} \pagepic{ps/v102padicintegercategory.ps}{PADICCT}{0.70} +<>= +)set break resume +)sys rm -f PAdicIntegerCategory.output +)spool PAdicIntegerCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PAdicIntegerCategory +--R PAdicIntegerCategory p: Integer is a category constructor +--R Abbreviation for PAdicIntegerCategory is PADICCT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PADICCT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R digits : % -> Stream Integer extend : (%,Integer) -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R moduloP : % -> Integer modulus : () -> Integer +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R ?quo? : (%,%) -> % quotientByP : % -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R sqrt : (%,Integer) -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R approximate : (%,Integer) -> Integer +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PAdicIntegerCategory examples +==================================================================== + +See Also: +o )show PAdicIntegerCategory + +@ {\bf See:} \pagefrom{CharacteristicZero}{CHARZ} @@ -45318,6 +55629,149 @@ digraph pic { \pagehead{PolynomialCategory}{POLYCAT} \pagepic{ps/v102polynomialcategory.ps}{POLYCAT}{0.40} +<>= +)set break resume +)sys rm -f PolynomialCategory.output +)spool PolynomialCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PolynomialCategory +--R PolynomialCategory(R: Ring,E: OrderedAbelianMonoidSup,VarSet: OrderedSet) is a category constructor +--R Abbreviation for PolynomialCategory is POLYCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for POLYCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List VarSet) -> % D : (%,VarSet) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coefficients : % -> List R coerce : VarSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> E +--R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % +--R eval : (%,VarSet,R) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R mapExponents : ((E -> E),%) -> % minimumDegree : % -> E +--R monomial : (R,E) -> % monomial? : % -> Boolean +--R monomials : % -> List % one? : % -> Boolean +--R pomopo! : (%,R,E,%) -> % primitiveMonomials : % -> List % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> VarSet retract : % -> R +--R sample : () -> % variables : % -> List VarSet +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List VarSet,List NonNegativeInteger) -> % +--R D : (%,VarSet,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ +--R coefficient : (%,List VarSet,List NonNegativeInteger) -> % +--R coefficient : (%,VarSet,NonNegativeInteger) -> % +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT +--R coerce : % -> % if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) +--R content : (%,VarSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if VarSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if VarSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if VarSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List VarSet) -> List NonNegativeInteger +--R degree : (%,VarSet) -> NonNegativeInteger +--R differentiate : (%,List VarSet,List NonNegativeInteger) -> % +--R differentiate : (%,VarSet,NonNegativeInteger) -> % +--R differentiate : (%,List VarSet) -> % +--R discriminant : (%,VarSet) -> % if R has COMRING +--R eval : (%,List VarSet,List %) -> % +--R eval : (%,List VarSet,List R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(VarSet,"failed") +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List VarSet) -> List NonNegativeInteger +--R minimumDegree : (%,VarSet) -> NonNegativeInteger +--R monicDivide : (%,%,VarSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List VarSet,List NonNegativeInteger) -> % +--R monomial : (%,VarSet,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,VarSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,VarSet) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if VarSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if VarSet has PATMAB FLOAT and R has PATMAB FLOAT +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,VarSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%,VarSet) -> % if R has COMRING +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(VarSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List VarSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,VarSet) -> SparseUnivariatePolynomial % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PolynomialCategory examples +==================================================================== + +See Also: +o )show PolynomialCategory + +@ {\bf See:} \pageto{DifferentialPolynomialCategory}{DPOLCAT} @@ -46236,6 +56690,137 @@ digraph pic { \pagehead{UnivariateTaylorSeriesCategory}{UTSCAT} \pagepic{ps/v102univariatetaylorseriescategory.ps}{UTSCAT}{0.60} +<>= +)set break resume +)sys rm -f UnivariateTaylorSeriesCategory.output +)spool UnivariateTaylorSeriesCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariateTaylorSeriesCategory +--R UnivariateTaylorSeriesCategory Coef: Ring is a category constructor +--R Abbreviation for UnivariateTaylorSeriesCategory is UTSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UTSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficients : % -> Stream Coef coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> NonNegativeInteger hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> NonNegativeInteger pole? : % -> Boolean +--R quoByVar : % -> % recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R series : Stream Coef -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Coef) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,NonNegativeInteger) -> Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,NonNegativeInteger) -> Coef +--R coerce : Coef -> % if Coef has COMRING +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef +--R ?.? : (%,%) -> % if NonNegativeInteger has SGROUP +--R ?.? : (%,NonNegativeInteger) -> Coef +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,NonNegativeInteger) -> % +--R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (Coef,NonNegativeInteger) -> % +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,NonNegativeInteger) -> NonNegativeInteger +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef +--R polynomial : (%,NonNegativeInteger) -> Polynomial Coef +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : Stream Record(k: NonNegativeInteger,c: Coef) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: NonNegativeInteger,c: Coef) +--R truncate : (%,NonNegativeInteger,NonNegativeInteger) -> % +--R truncate : (%,NonNegativeInteger) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariateTaylorSeriesCategory examples +==================================================================== + +See Also: +o )show UnivariateTaylorSeriesCategory + +@ {\bf See:} \pagefrom{RadicalCategory}{RADCAT} @@ -46890,6 +57475,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{AlgebraicallyClosedField}{ACF} \pagepic{ps/v102algebraicallyclosedfield.ps}{ACF}{0.75} + <>= )set break resume )sys rm -f AlgebraicallyClosedField.output @@ -47526,6 +58112,180 @@ digraph pic { \pagehead{DifferentialPolynomialCategory}{DPOLCAT} \pagepic{ps/v102differentialpolynomialcategory.ps}{DPOLCAT}{0.35} +<>= +)set break resume +)sys rm -f DifferentialPolynomialCategory.output +)spool DifferentialPolynomialCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DifferentialPolynomialCategory +--R DifferentialPolynomialCategory(R: Ring,S: OrderedSet,V: DifferentialVariableCategory t#2,E: OrderedAbelianMonoidSup) is a category constructor +--R Abbreviation for DifferentialPolynomialCategory is DPOLCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DPOLCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R D : (%,List V) -> % D : (%,V) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coefficients : % -> List R coerce : S -> % +--R coerce : V -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> E differentiate : (%,List V) -> % +--R differentiate : (%,V) -> % eval : (%,List V,List %) -> % +--R eval : (%,V,%) -> % eval : (%,List V,List R) -> % +--R eval : (%,V,R) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R initial : % -> % isobaric? : % -> Boolean +--R latex : % -> String leader : % -> V +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R map : ((R -> R),%) -> % mapExponents : ((E -> E),%) -> % +--R minimumDegree : % -> E monomial : (R,E) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R pomopo! : (%,R,E,%) -> % primitiveMonomials : % -> List % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> S retract : % -> V +--R retract : % -> R sample : () -> % +--R separant : % -> % variables : % -> List V +--R weight : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,List V,List NonNegativeInteger) -> % +--R D : (%,V,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ +--R coefficient : (%,List V,List NonNegativeInteger) -> % +--R coefficient : (%,V,NonNegativeInteger) -> % +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) +--R content : (%,V) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if V has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if V has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if V has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,S) -> NonNegativeInteger +--R degree : (%,List V) -> List NonNegativeInteger +--R degree : (%,V) -> NonNegativeInteger +--R differentialVariables : % -> List S +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,List V,List NonNegativeInteger) -> % +--R differentiate : (%,V,NonNegativeInteger) -> % +--R discriminant : (%,V) -> % if R has COMRING +--R eval : (%,List S,List R) -> % if R has DIFRING +--R eval : (%,S,R) -> % if R has DIFRING +--R eval : (%,List S,List %) -> % if R has DIFRING +--R eval : (%,S,%) -> % if R has DIFRING +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(V,"failed") +--R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING +--R makeVariable : S -> (NonNegativeInteger -> %) +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List V) -> List NonNegativeInteger +--R minimumDegree : (%,V) -> NonNegativeInteger +--R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %) +--R monomial : (%,List V,List NonNegativeInteger) -> % +--R monomial : (%,V,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,V) -> % +--R multivariate : (SparseUnivariatePolynomial R,V) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,S) -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB FLOAT and R has PATMAB FLOAT +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,V) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%,V) -> % if R has COMRING +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(S,"failed") +--R retractIfCan : % -> Union(V,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List V) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,V) -> SparseUnivariatePolynomial % +--R weight : (%,S) -> NonNegativeInteger +--R weights : (%,S) -> List NonNegativeInteger +--R weights : % -> List NonNegativeInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DifferentialPolynomialCategory examples +==================================================================== + +See Also: +o )show DifferentialPolynomialCategory + +@ {\bf See:} \pagefrom{DifferentialExtension}{DIFEXT} @@ -48238,6 +58998,78 @@ digraph pic { \pagehead{FieldOfPrimeCharacteristic}{FPC} \pagepic{ps/v102fieldofprimecharacteristic.ps}{FPC}{1.00} +<>= +)set break resume +)sys rm -f FieldOfPrimeCharacteristic.output +)spool FieldOfPrimeCharacteristic.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FieldOfPrimeCharacteristic +--R FieldOfPrimeCharacteristic is a category constructor +--R Abbreviation for FieldOfPrimeCharacteristic is FPC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FPC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R prime? : % -> Boolean primeFrobenius : % -> % +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R order : % -> OnePointCompletion PositiveInteger +--R primeFrobenius : (%,NonNegativeInteger) -> % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FieldOfPrimeCharacteristic examples +==================================================================== + +See Also: +o )show FieldOfPrimeCharacteristic + +@ {\bf See:} \pageto{FiniteFieldCategory}{FFIELDC} @@ -48483,6 +59315,64 @@ digraph pic { \pagehead{FiniteRankAlgebra}{FINRALG} \pagepic{ps/v102finiterankalgebra.ps}{FINRALG}{0.50} +<>= +)set break resume +)sys rm -f FiniteRankAlgebra.output +)spool FiniteRankAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteRankAlgebra +--R FiniteRankAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory t#1) is a category constructor +--R Abbreviation for FiniteRankAlgebra is FINRALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FINRALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R discriminant : Vector % -> R hash : % -> SingleInteger +--R latex : % -> String norm : % -> R +--R one? : % -> Boolean rank : () -> PositiveInteger +--R recip : % -> Union(%,"failed") sample : () -> % +--R trace : % -> R zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UP +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R minimalPolynomial : % -> UP if R has FIELD +--R regularRepresentation : (%,Vector %) -> Matrix R +--R represents : (Vector R,Vector %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R traceMatrix : Vector % -> Matrix R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteRankAlgebra examples +==================================================================== + +See Also: +o )show FiniteRankAlgebra + +@ {\bf See:} \pageto{FramedAlgebra}{FRAMALG} @@ -48745,6 +59635,198 @@ digraph pic { \pagehead{FunctionSpace}{FS} \pagepic{ps/v102functionspace.ps}{FS}{0.65} +<>= +)set break resume +)sys rm -f FunctionSpace.output +)spool FunctionSpace.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FunctionSpace +--R FunctionSpace R: OrderedSet is a category constructor +--R Abbreviation for FunctionSpace is FS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FS +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % if R has SGROUP 0 : () -> % if R has ABELSG +--R applyQuote : (Symbol,%,%) -> % applyQuote : (Symbol,%) -> % +--R belong? : BasicOperator -> Boolean box : List % -> % +--R box : % -> % coerce : R -> % +--R coerce : Symbol -> % coerce : Kernel % -> % +--R coerce : % -> OutputForm distribute : (%,%) -> % +--R distribute : % -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % eval : (%,Kernel %,%) -> % +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R kernels : % -> List Kernel % latex : % -> String +--R map : ((% -> %),Kernel %) -> % max : (%,%) -> % +--R min : (%,%) -> % paren : List % -> % +--R paren : % -> % retract : % -> R +--R retract : % -> Symbol retract : % -> Kernel % +--R subst : (%,Equation %) -> % tower : % -> List Kernel % +--R variables : % -> List Symbol ?~=? : (%,%) -> Boolean +--R ?*? : (%,%) -> % if R has SGROUP +--R ?*? : (PositiveInteger,%) -> % if R has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if R has ABELSG +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?*? : (%,R) -> % if R has COMRING +--R ?*? : (R,%) -> % if R has COMRING +--R ?*? : (%,Fraction Integer) -> % if R has INTDOM +--R ?*? : (Fraction Integer,%) -> % if R has INTDOM +--R ?**? : (%,PositiveInteger) -> % if R has SGROUP +--R ?**? : (%,NonNegativeInteger) -> % if R has SGROUP +--R ?**? : (%,Integer) -> % if R has GROUP or R has INTDOM +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has ABELGRP +--R ?/? : (%,%) -> % if R has GROUP or R has INTDOM +--R ?/? : (SparseMultivariatePolynomial(R,Kernel %),SparseMultivariatePolynomial(R,Kernel %)) -> % if R has INTDOM +--R D : (%,Symbol) -> % if R has RING +--R D : (%,List Symbol) -> % if R has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if R has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has RING +--R ?^? : (%,PositiveInteger) -> % if R has SGROUP +--R ?^? : (%,NonNegativeInteger) -> % if R has SGROUP +--R ?^? : (%,Integer) -> % if R has GROUP or R has INTDOM +--R applyQuote : (Symbol,List %) -> % +--R applyQuote : (Symbol,%,%,%,%) -> % +--R applyQuote : (Symbol,%,%,%) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R characteristic : () -> NonNegativeInteger if R has RING +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Integer -> % if R has RING or R has RETRACT INT +--R coerce : Fraction Integer -> % if R has INTDOM or R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT +--R coerce : Polynomial R -> % if R has RING +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Polynomial R -> % if R has INTDOM +--R coerce : Fraction Polynomial Fraction R -> % if R has INTDOM +--R coerce : Polynomial Fraction R -> % if R has INTDOM +--R coerce : Fraction R -> % if R has INTDOM +--R coerce : SparseMultivariatePolynomial(R,Kernel %) -> % if R has RING +--R commutator : (%,%) -> % if R has GROUP +--R conjugate : (%,%) -> % if R has GROUP +--R convert : % -> InputForm if R has KONVERT INFORM +--R convert : Factored % -> % if R has INTDOM +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT +--R definingPolynomial : % -> % if $ has RING +--R denom : % -> SparseMultivariatePolynomial(R,Kernel %) if R has INTDOM +--R denominator : % -> % if R has INTDOM +--R differentiate : (%,Symbol) -> % if R has RING +--R differentiate : (%,List Symbol) -> % if R has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has RING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % +--R euclideanSize : % -> NonNegativeInteger if R has INTDOM +--R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING +--R eval : (%,Symbol,NonNegativeInteger,(List % -> %)) -> % if R has RING +--R eval : (%,List Symbol,List NonNegativeInteger,List (List % -> %)) -> % if R has RING +--R eval : (%,List Symbol,List NonNegativeInteger,List (% -> %)) -> % if R has RING +--R eval : (%,List BasicOperator,List %,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT INFORM +--R eval : % -> % if R has KONVERT INFORM +--R eval : (%,List Symbol) -> % if R has KONVERT INFORM +--R eval : (%,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Kernel %,List %) -> % +--R even? : % -> Boolean if $ has RETRACT INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has INTDOM +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has INTDOM +--R factor : % -> Factored % if R has INTDOM +--R gcd : (%,%) -> % if R has INTDOM +--R gcd : List % -> % if R has INTDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has INTDOM +--R inv : % -> % if R has GROUP or R has INTDOM +--R is? : (%,BasicOperator) -> Boolean +--R isExpt : (%,Symbol) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING +--R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING +--R isExpt : % -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has SGROUP +--R isMult : % -> Union(Record(coef: Integer,var: Kernel %),"failed") if R has ABELSG +--R isPlus : % -> Union(List %,"failed") if R has ABELSG +--R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING +--R isTimes : % -> Union(List %,"failed") if R has SGROUP +--R kernel : (BasicOperator,List %) -> % +--R lcm : (%,%) -> % if R has INTDOM +--R lcm : List % -> % if R has INTDOM +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has INTDOM +--R numer : % -> SparseMultivariatePolynomial(R,Kernel %) if R has RING +--R numerator : % -> % if R has RING +--R odd? : % -> Boolean if $ has RETRACT INT +--R one? : % -> Boolean if R has SGROUP +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT +--R prime? : % -> Boolean if R has INTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has INTDOM +--R ?quo? : (%,%) -> % if R has INTDOM +--R recip : % -> Union(%,"failed") if R has SGROUP +--R reducedSystem : Matrix % -> Matrix R if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring)) +--R reducedSystem : Matrix % -> Matrix Integer if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring)) +--R ?rem? : (%,%) -> % if R has INTDOM +--R retract : % -> Fraction Integer if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT +--R retract : % -> Polynomial R if R has RING +--R retract : % -> Fraction Polynomial R if R has INTDOM +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Polynomial R,"failed") if R has RING +--R retractIfCan : % -> Union(Fraction Polynomial R,"failed") if R has INTDOM +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(Kernel %,"failed") +--R sample : () -> % if R has SGROUP or R has ABELSG +--R sizeLess? : (%,%) -> Boolean if R has INTDOM +--R squareFree : % -> Factored % if R has INTDOM +--R squareFreePart : % -> % if R has INTDOM +--R subst : (%,List Kernel %,List %) -> % +--R subst : (%,List Equation %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : (%,Kernel %) -> Fraction SparseUnivariatePolynomial % if R has INTDOM +--R zero? : % -> Boolean if R has ABELSG +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FunctionSpace examples +==================================================================== + +See Also: +o )show FunctionSpace + +@ {\bf See:} \pagefrom{AbelianGroup}{ABELGRP} @@ -50006,6 +61088,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{InfinitlyClosePointCategory}{INFCLCT} \pagepic{ps/v102infinitlyclosepointcategory.eps}{INFCLCT}{0.50} + <>= )set break resume )sys rm -f InfinitlyClosePointCategory.output @@ -50261,6 +61344,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{PseudoAlgebraicClosureOfPerfectFieldCategory}{PACPERC} \pagepic{ps/v102pseudoalgebraicclosureofperfectfieldcategory.ps}{PACPERC}{0.50} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfPerfectFieldCategory.output @@ -50616,6 +61700,140 @@ digraph pic { \pagehead{QuotientFieldCategory}{QFCAT} \pagepic{ps/v102quotientfieldcategory.ps}{QFCAT}{0.50} +<>= +)set break resume +)sys rm -f QuotientFieldCategory.output +)spool QuotientFieldCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show QuotientFieldCategory +--R QuotientFieldCategory S: IntegralDomain is a category constructor +--R Abbreviation for QuotientFieldCategory is QFCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for QFCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (S,%) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (S,S) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : (%,(S -> S)) -> % +--R D : % -> % if S has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R ceiling : % -> S if S has INS coerce : S -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denom : % -> S denominator : % -> % +--R factor : % -> Factored % floor : % -> S if S has INS +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger init : () -> % if S has STEP +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R map : ((S -> S),%) -> % numer : % -> S +--R numerator : % -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R random : () -> % if S has INS recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> S +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R D : (%,(S -> S),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL +--R D : (%,List Symbol) -> % if S has PDRING SYMBOL +--R D : (%,Symbol) -> % if S has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if S has DIFRING +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if S has OINTDOM +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if S has CHARNZ or and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit)) +--R coerce : Symbol -> % if S has RETRACT SYMBOL +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit)) +--R convert : % -> DoubleFloat if S has REAL +--R convert : % -> Float if S has REAL +--R convert : % -> InputForm if S has KONVERT INFORM +--R convert : % -> Pattern Float if S has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if S has KONVERT PATTERN INT +--R differentiate : (%,(S -> S)) -> % +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING +--R differentiate : % -> % if S has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,S) -> % if S has ELTAB(S,S) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,S) -> % if S has IEVALAB(SYMBOL,S) +--R eval : (%,List Symbol,List S) -> % if S has IEVALAB(SYMBOL,S) +--R eval : (%,List Equation S) -> % if S has EVALAB S +--R eval : (%,Equation S) -> % if S has EVALAB S +--R eval : (%,S,S) -> % if S has EVALAB S +--R eval : (%,List S,List S) -> % if S has EVALAB S +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if S has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if S has PFECAT +--R fractionPart : % -> % if S has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R negative? : % -> Boolean if S has OINTDOM +--R nextItem : % -> Union(%,"failed") if S has STEP +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if S has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if S has PATMAB INT +--R positive? : % -> Boolean if S has OINTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R reducedSystem : Matrix % -> Matrix S +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT +--R retract : % -> Integer if S has RETRACT INT +--R retract : % -> Fraction Integer if S has RETRACT INT +--R retract : % -> Symbol if S has RETRACT SYMBOL +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT INT +--R retractIfCan : % -> Union(Symbol,"failed") if S has RETRACT SYMBOL +--R retractIfCan : % -> Union(S,"failed") +--R sign : % -> Integer if S has OINTDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if S has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if S has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> S if S has EUCDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +QuotientFieldCategory examples +==================================================================== + +See Also: +o )show QuotientFieldCategory + +@ {\bf See:} \pagefrom{Algebra}{ALGEBRA} @@ -51187,6 +62405,104 @@ digraph pic { \pagehead{RealClosedField}{RCFIELD} \pagepic{ps/v102realclosedfield.ps}{RCFIELD}{0.50} +<>= +)set break resume +)sys rm -f RealClosedField.output +)spool RealClosedField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RealClosedField +--R RealClosedField is a category constructor +--R Abbreviation for RealClosedField is RCFIELD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RCFIELD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> % +--R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R coerce : Integer -> % coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Fraction Integer -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored % gcd : (%,%) -> % +--R gcd : List % -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : (%,%) -> % lcm : List % -> % +--R max : (%,%) -> % min : (%,%) -> % +--R negative? : % -> Boolean nthRoot : (%,Integer) -> % +--R one? : % -> Boolean positive? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R rename : (%,OutputForm) -> % rename! : (%,OutputForm) -> % +--R retract : % -> Fraction Integer sample : () -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R sqrt : Integer -> % sqrt : Fraction Integer -> % +--R sqrt : % -> % squareFree : % -> Factored % +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R allRootsOf : Polynomial Integer -> List % +--R allRootsOf : Polynomial Fraction Integer -> List % +--R allRootsOf : Polynomial % -> List % +--R allRootsOf : SparseUnivariatePolynomial Integer -> List % +--R allRootsOf : SparseUnivariatePolynomial Fraction Integer -> List % +--R allRootsOf : SparseUnivariatePolynomial % -> List % +--R approximate : (%,%) -> Fraction Integer +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R mainDefiningPolynomial : % -> Union(SparseUnivariatePolynomial %,"failed") +--R mainForm : % -> Union(OutputForm,"failed") +--R mainValue : % -> Union(SparseUnivariatePolynomial %,"failed") +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R retract : % -> Fraction Integer if Fraction Integer has RETRACT FRAC INT +--R retract : % -> Integer if Fraction Integer has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction Integer has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if Fraction Integer has RETRACT INT +--R rootOf : (SparseUnivariatePolynomial %,PositiveInteger) -> Union(%,"failed") +--R rootOf : (SparseUnivariatePolynomial %,PositiveInteger,OutputForm) -> Union(%,"failed") +--R sqrt : (%,NonNegativeInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RealClosedField examples +==================================================================== + +See Also: +o )show RealClosedField + +@ {\bf See:} \pagefrom{Algebra}{ALGEBRA} @@ -51641,6 +62957,90 @@ digraph pic { \pagehead{RealNumberSystem}{RNS} \pagepic{ps/v102realnumbersystem.ps}{RNS}{0.50} +<>= +)set break resume +)sys rm -f RealNumberSystem.output +)spool RealNumberSystem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RealNumberSystem +--R RealNumberSystem is a category constructor +--R Abbreviation for RealNumberSystem is RNS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RNS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R associates? : (%,%) -> Boolean ceiling : % -> % +--R coerce : Fraction Integer -> % coerce : Integer -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Pattern Float convert : % -> DoubleFloat +--R convert : % -> Float factor : % -> Factored % +--R floor : % -> % fractionPart : % -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R norm : % -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean positive? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction Integer retract : % -> Integer +--R round : % -> % sample : () -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R sqrt : % -> % squareFree : % -> Factored % +--R squareFreePart : % -> % truncate : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> Integer zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RealNumberSystem examples +==================================================================== + +See Also: +o )show RealNumberSystem + +@ {\bf See:} \pageto{FloatingPointSystem}{FPS} @@ -51989,6 +63389,208 @@ digraph pic { \pagehead{RecursivePolynomialCategory}{RPOLCAT} \pagepic{ps/v102recursivepolynomialcategory.ps}{RPOLCAT}{0.30} +<>= +)set break resume +)sys rm -f RecursivePolynomialCategory.output +)spool RecursivePolynomialCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RecursivePolynomialCategory +--R RecursivePolynomialCategory(R: Ring,E: OrderedAbelianMonoidSup,V: OrderedSet) is a category constructor +--R Abbreviation for RecursivePolynomialCategory is RPOLCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RPOLCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List V) -> % D : (%,V) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coefficients : % -> List R coerce : V -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm deepestInitial : % -> % +--R deepestTail : % -> % degree : % -> E +--R differentiate : (%,List V) -> % differentiate : (%,V) -> % +--R eval : (%,List V,List %) -> % eval : (%,V,%) -> % +--R eval : (%,List V,List R) -> % eval : (%,V,R) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger head : % -> % +--R headReduce : (%,%) -> % headReduced? : (%,%) -> Boolean +--R infRittWu? : (%,%) -> Boolean init : % -> % +--R initiallyReduce : (%,%) -> % iteratedInitials : % -> List % +--R latex : % -> String lazyPquo : (%,%,V) -> % +--R lazyPquo : (%,%) -> % lazyPrem : (%,%,V) -> % +--R lazyPrem : (%,%) -> % leadingCoefficient : (%,V) -> % +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R leastMonomial : % -> % mainCoefficients : % -> List % +--R mainMonomial : % -> % mainMonomials : % -> List % +--R map : ((R -> R),%) -> % mapExponents : ((E -> E),%) -> % +--R mdeg : % -> NonNegativeInteger minimumDegree : % -> E +--R monic? : % -> Boolean monicModulo : (%,%) -> % +--R monomial : (R,E) -> % monomial? : % -> Boolean +--R monomials : % -> List % mvar : % -> V +--R normalized? : (%,%) -> Boolean one? : % -> Boolean +--R pomopo! : (%,R,E,%) -> % pquo : (%,%,V) -> % +--R pquo : (%,%) -> % prem : (%,%,V) -> % +--R prem : (%,%) -> % primitiveMonomials : % -> List % +--R quasiMonic? : % -> Boolean recip : % -> Union(%,"failed") +--R reduced? : (%,List %) -> Boolean reduced? : (%,%) -> Boolean +--R reductum : (%,V) -> % reductum : % -> % +--R retract : % -> V retract : % -> R +--R sample : () -> % supRittWu? : (%,%) -> Boolean +--R tail : % -> % variables : % -> List V +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List V,List NonNegativeInteger) -> % +--R D : (%,V,NonNegativeInteger) -> % +--R LazardQuotient : (%,%,NonNegativeInteger) -> % if R has INTDOM +--R LazardQuotient2 : (%,%,%,NonNegativeInteger) -> % if R has INTDOM +--R RittWuCompare : (%,%) -> Union(Boolean,"failed") +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ +--R coefficient : (%,List V,List NonNegativeInteger) -> % +--R coefficient : (%,V,NonNegativeInteger) -> % +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT +--R coerce : % -> Polynomial R if V has KONVERT SYMBOL +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) +--R content : (%,V) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> Polynomial R if V has KONVERT SYMBOL +--R convert : % -> String if R has RETRACT INT and V has KONVERT SYMBOL +--R convert : Polynomial R -> % if V has KONVERT SYMBOL +--R convert : Polynomial Integer -> % if not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R convert : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R convert : % -> InputForm if V has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if V has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if V has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List V) -> List NonNegativeInteger +--R degree : (%,V) -> NonNegativeInteger +--R differentiate : (%,List V,List NonNegativeInteger) -> % +--R differentiate : (%,V,NonNegativeInteger) -> % +--R discriminant : (%,V) -> % if R has COMRING +--R exactQuotient : (%,%) -> % if R has INTDOM +--R exactQuotient : (%,R) -> % if R has INTDOM +--R exactQuotient! : (%,%) -> % if R has INTDOM +--R exactQuotient! : (%,R) -> % if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedSubResultantGcd : (%,%) -> Record(gcd: %,coef1: %,coef2: %) if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcd : (R,%) -> R if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM +--R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM +--R headReduced? : (%,List %) -> Boolean +--R initiallyReduced? : (%,List %) -> Boolean +--R initiallyReduced? : (%,%) -> Boolean +--R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lastSubResultant : (%,%) -> % if R has INTDOM +--R lazyPremWithDefault : (%,%,V) -> Record(coef: %,gap: NonNegativeInteger,remainder: %) +--R lazyPremWithDefault : (%,%) -> Record(coef: %,gap: NonNegativeInteger,remainder: %) +--R lazyPseudoDivide : (%,%,V) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) +--R lazyPseudoDivide : (%,%) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) +--R lazyResidueClass : (%,%) -> Record(polnum: %,polden: %,power: NonNegativeInteger) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainContent : % -> % if R has GCDDOM +--R mainPrimitivePart : % -> % if R has GCDDOM +--R mainSquareFreePart : % -> % if R has GCDDOM +--R mainVariable : % -> Union(V,"failed") +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List V) -> List NonNegativeInteger +--R minimumDegree : (%,V) -> NonNegativeInteger +--R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %) +--R monomial : (%,List V,List NonNegativeInteger) -> % +--R monomial : (%,V,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,V) -> % +--R multivariate : (SparseUnivariatePolynomial R,V) -> % +--R nextsubResultant2 : (%,%,%,%) -> % if R has INTDOM +--R normalized? : (%,List %) -> Boolean +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB FLOAT and R has PATMAB FLOAT +--R primPartElseUnitCanonical : % -> % if R has INTDOM +--R primPartElseUnitCanonical! : % -> % if R has INTDOM +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,V) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R primitivePart! : % -> % if R has GCDDOM +--R pseudoDivide : (%,%) -> Record(quotient: %,remainder: %) +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%) -> % if R has INTDOM +--R resultant : (%,%,V) -> % if R has COMRING +--R retract : Polynomial R -> % if not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) and V has KONVERT SYMBOL or not has(R,IntegerNumberSystem) and not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or not has(R,QuotientFieldCategory Integer) and R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R retract : Polynomial Integer -> % if not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R retract : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : Polynomial R -> Union(%,"failed") if not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) and V has KONVERT SYMBOL or not has(R,IntegerNumberSystem) and not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or not has(R,QuotientFieldCategory Integer) and R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R retractIfCan : Polynomial Integer -> Union(%,"failed") if not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R retractIfCan : Polynomial Fraction Integer -> Union(%,"failed") if R has ALGEBRA FRAC INT and V has KONVERT SYMBOL +--R retractIfCan : % -> Union(V,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantChain : (%,%) -> List % if R has INTDOM +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List V) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,V) -> SparseUnivariatePolynomial % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RecursivePolynomialCategory examples +==================================================================== + +See Also: +o )show RecursivePolynomialCategory + +@ {\bf See:} \pagefrom{PolynomialCategory}{POLYCAT} @@ -53768,6 +65370,155 @@ digraph pic { \pagehead{UnivariateLaurentSeriesCategory}{ULSCAT} \pagepic{ps/v102univariatelaurentseriescategory.ps}{ULSCAT}{0.50} +<>= +)set break resume +)sys rm -f UnivariateLaurentSeriesCategory.output +)spool UnivariateLaurentSeriesCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariateLaurentSeriesCategory +--R UnivariateLaurentSeriesCategory Coef: Ring is a category constructor +--R Abbreviation for UnivariateLaurentSeriesCategory is ULSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ULSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficient : (%,Integer) -> Coef coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Integer ?.? : (%,Integer) -> Coef +--R extend : (%,Integer) -> % hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial : (Coef,Integer) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : (%,Integer) -> Integer +--R order : % -> Integer pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % truncate : (%,Integer) -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : % -> % if Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,%) -> % if Integer has SGROUP +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R ?quo? : (%,%) -> % if Coef has FIELD +--R rationalFunction : (%,Integer,Integer) -> Fraction Polynomial Coef if Coef has INTDOM +--R rationalFunction : (%,Integer) -> Fraction Polynomial Coef if Coef has INTDOM +--R ?rem? : (%,%) -> % if Coef has FIELD +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : Stream Record(k: Integer,c: Coef) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: Integer,c: Coef) +--R truncate : (%,Integer,Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariateLaurentSeriesCategory examples +==================================================================== + +See Also: +o )show UnivariateLaurentSeriesCategory + +@ {\bf See:} \pageto{UnivariateLaurentSeriesConstructorCategory}{ULSCCAT} @@ -54250,6 +66001,156 @@ digraph pic { \pagehead{UnivariatePuiseuxSeriesCategory}{UPXSCAT} \pagepic{ps/v102univariatepuiseuxseriescategory.ps}{UPXSCAT}{0.50} +<>= +)set break resume +)sys rm -f UnivariatePuiseuxSeriesCategory.output +)spool UnivariatePuiseuxSeriesCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariatePuiseuxSeriesCategory +--R UnivariatePuiseuxSeriesCategory Coef: Ring is a category constructor +--R Abbreviation for UnivariatePuiseuxSeriesCategory is UPXSCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPXSCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> Fraction Integer +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : % -> Fraction Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,Fraction Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,%) -> % if Fraction Integer has SGROUP +--R ?.? : (%,Fraction Integer) -> Coef +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,Fraction Integer) -> % +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % +--R monomial : (Coef,Fraction Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyExponents : (%,Fraction Integer) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,Fraction Integer) -> Fraction Integer +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R ?quo? : (%,%) -> % if Coef has FIELD +--R ?rem? : (%,%) -> % if Coef has FIELD +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: Fraction Integer,c: Coef) +--R truncate : (%,Fraction Integer,Fraction Integer) -> % +--R truncate : (%,Fraction Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariatePuiseuxSeriesCategory examples +==================================================================== + +See Also: +o )show UnivariatePuiseuxSeriesCategory + +@ {\bf See:} \pageto{UnivariatePuiseuxSeriesConstructorCategory}{UPXSCCA} @@ -54716,6 +66617,206 @@ digraph pic { \pagehead{UnivariatePolynomialCategory}{UPOLYC} \pagepic{ps/v102univariatepolynomialcategory.ps}{UPOLYC}{0.35} +<>= +)set break resume +)sys rm -f UnivariatePolynomialCategory.output +)spool UnivariatePolynomialCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariatePolynomialCategory +--R UnivariatePolynomialCategory R: Ring is a category constructor +--R Abbreviation for UnivariatePolynomialCategory is UPOLYC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPOLYC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean primitiveMonomials : % -> List % +--R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,SingletonAsOrderedSet) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ +--R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT +--R coerce : SingletonAsOrderedSet -> % +--R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM +--R elt : (Fraction %,R) -> R if R has FIELD +--R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R integrate : % -> % if R has ALGEBRA FRAC INT +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial R +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R ?rem? : (%,%) -> % if R has FIELD +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % +--R unmakeSUP : SparseUnivariatePolynomial R -> % +--R variables : % -> List SingletonAsOrderedSet +--R vectorise : (%,NonNegativeInteger) -> Vector R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariatePolynomialCategory examples +==================================================================== + +See Also: +o )show UnivariatePolynomialCategory + +@ {\bf See:} \pagefrom{Algebra}{ALGEBRA} @@ -55703,6 +67804,197 @@ digraph pic { \pagehead{AlgebraicallyClosedFunctionSpace}{ACFS} \pagepic{ps/v102algebraicallyclosedfunctionspace.ps}{ACFS}{0.45} +<>= +)set break resume +)sys rm -f AlgebraicallyClosedFunctionSpace.output +)spool AlgebraicallyClosedFunctionSpace.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AlgebraicallyClosedFunctionSpace +--R AlgebraicallyClosedFunctionSpace R: Join(OrderedSet,IntegralDomain) is a category constructor +--R Abbreviation for AlgebraicallyClosedFunctionSpace is ACFS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ACFS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % applyQuote : (Symbol,%) -> % +--R applyQuote : (Symbol,%,%) -> % associates? : (%,%) -> Boolean +--R belong? : BasicOperator -> Boolean box : % -> % +--R box : List % -> % coerce : Kernel % -> % +--R coerce : Symbol -> % coerce : R -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R distribute : % -> % distribute : (%,%) -> % +--R elt : (BasicOperator,%) -> % elt : (BasicOperator,%,%) -> % +--R eval : (%,Kernel %,%) -> % eval : (%,List Equation %) -> % +--R eval : (%,Equation %) -> % eval : (%,%,%) -> % +--R eval : (%,List %,List %) -> % factor : % -> Factored % +--R freeOf? : (%,%) -> Boolean freeOf? : (%,Symbol) -> Boolean +--R gcd : List % -> % gcd : (%,%) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R inv : % -> % is? : (%,Symbol) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % map : ((% -> %),Kernel %) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R nthRoot : (%,Integer) -> % one? : % -> Boolean +--R paren : % -> % paren : List % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Kernel % retract : % -> Symbol +--R retract : % -> R rootOf : (%,Symbol) -> % +--R rootOf : % -> % rootOf : Polynomial % -> % +--R rootsOf : (%,Symbol) -> List % rootsOf : % -> List % +--R rootsOf : Polynomial % -> List % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : % -> % +--R squareFree : % -> Factored % squareFreePart : % -> % +--R subst : (%,Equation %) -> % tower : % -> List Kernel % +--R unit? : % -> Boolean unitCanonical : % -> % +--R variables : % -> List Symbol zero? : % -> Boolean +--R zeroOf : (%,Symbol) -> % zeroOf : % -> % +--R zeroOf : Polynomial % -> % zerosOf : (%,Symbol) -> List % +--R zerosOf : % -> List % zerosOf : Polynomial % -> List % +--R ?~=? : (%,%) -> Boolean +--R ?*? : (R,%) -> % if R has COMRING +--R ?*? : (%,R) -> % if R has COMRING +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (SparseMultivariatePolynomial(R,Kernel %),SparseMultivariatePolynomial(R,Kernel %)) -> % if R has INTDOM +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if R has RING +--R D : (%,List Symbol) -> % if R has RING +--R D : (%,Symbol) -> % if R has RING +--R ?^? : (%,NonNegativeInteger) -> % +--R applyQuote : (Symbol,%,%,%) -> % +--R applyQuote : (Symbol,%,%,%,%) -> % +--R applyQuote : (Symbol,List %) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : SparseMultivariatePolynomial(R,Kernel %) -> % if R has RING +--R coerce : Fraction R -> % if R has INTDOM +--R coerce : Polynomial Fraction R -> % if R has INTDOM +--R coerce : Fraction Polynomial Fraction R -> % if R has INTDOM +--R coerce : Fraction Polynomial R -> % if R has INTDOM +--R coerce : Polynomial R -> % if R has RING +--R commutator : (%,%) -> % if R has GROUP +--R conjugate : (%,%) -> % if R has GROUP +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT +--R convert : Factored % -> % if R has INTDOM +--R convert : % -> InputForm if R has KONVERT INFORM +--R definingPolynomial : % -> % if $ has RING +--R denom : % -> SparseMultivariatePolynomial(R,Kernel %) if R has INTDOM +--R denominator : % -> % if R has INTDOM +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has RING +--R differentiate : (%,List Symbol) -> % if R has RING +--R differentiate : (%,Symbol) -> % if R has RING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R elt : (BasicOperator,%,%,%) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,List %) -> % +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,List Kernel %,List %) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,List Symbol) -> % if R has KONVERT INFORM +--R eval : % -> % if R has KONVERT INFORM +--R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,List BasicOperator,List %,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,List Symbol,List NonNegativeInteger,List (% -> %)) -> % if R has RING +--R eval : (%,List Symbol,List NonNegativeInteger,List (List % -> %)) -> % if R has RING +--R eval : (%,Symbol,NonNegativeInteger,(List % -> %)) -> % if R has RING +--R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING +--R even? : % -> Boolean if $ has RETRACT INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R is? : (%,BasicOperator) -> Boolean +--R isExpt : % -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has SGROUP +--R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING +--R isExpt : (%,Symbol) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING +--R isMult : % -> Union(Record(coef: Integer,var: Kernel %),"failed") if R has ABELSG +--R isPlus : % -> Union(List %,"failed") if R has ABELSG +--R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING +--R isTimes : % -> Union(List %,"failed") if R has SGROUP +--R kernel : (BasicOperator,List %) -> % +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R numer : % -> SparseMultivariatePolynomial(R,Kernel %) if R has RING +--R numerator : % -> % if R has RING +--R odd? : % -> Boolean if $ has RETRACT INT +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R reducedSystem : Matrix % -> Matrix Integer if and(has(R,Ring),has(R,LinearlyExplicitRingOver Integer)) or and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring)) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(R,Ring),has(R,LinearlyExplicitRingOver Integer)) or and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring)) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING +--R reducedSystem : Matrix % -> Matrix R if R has RING +--R retract : % -> Fraction Integer if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Polynomial R if R has INTDOM +--R retract : % -> Polynomial R if R has RING +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Kernel %,"failed") +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Polynomial R,"failed") if R has INTDOM +--R retractIfCan : % -> Union(Polynomial R,"failed") if R has RING +--R rootOf : (SparseUnivariatePolynomial %,Symbol) -> % +--R rootOf : SparseUnivariatePolynomial % -> % +--R rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R rootsOf : SparseUnivariatePolynomial % -> List % +--R subst : (%,List Equation %) -> % +--R subst : (%,List Kernel %,List %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R univariate : (%,Kernel %) -> Fraction SparseUnivariatePolynomial % if R has INTDOM +--R zeroOf : (SparseUnivariatePolynomial %,Symbol) -> % +--R zeroOf : SparseUnivariatePolynomial % -> % +--R zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R zerosOf : SparseUnivariatePolynomial % -> List % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AlgebraicallyClosedFunctionSpace examples +==================================================================== + +See Also: +o )show AlgebraicallyClosedFunctionSpace + +@ {\bf See:} \pagefrom{AlgebraicallyClosedField}{ACF} @@ -56281,6 +68573,89 @@ digraph pic { \pagehead{ExtensionField}{XF} \pagepic{ps/v102extensionfield.ps}{XF}{0.75} +<>= +)set break resume +)sys rm -f ExtensionField.output +)spool ExtensionField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ExtensionField +--R ExtensionField F: Field is a category constructor +--R Abbreviation for ExtensionField is XF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for XF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (F,%) -> % ?*? : (%,F) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,F) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean coerce : F -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> F +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R Frobenius : (%,NonNegativeInteger) -> % if F has FINITE +--R Frobenius : % -> % if F has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if F has CHARNZ or F has FINITE +--R degree : % -> OnePointCompletion PositiveInteger +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if F has CHARNZ or F has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R order : % -> OnePointCompletion PositiveInteger if F has CHARNZ or F has FINITE +--R primeFrobenius : % -> % if F has CHARNZ or F has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if F has CHARNZ or F has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R retractIfCan : % -> Union(F,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ExtensionField examples +==================================================================== + +See Also: +o )show ExtensionField + +@ {\bf See:} \pageto{FiniteAlgebraicExtensionField}{FAXF} @@ -56608,6 +68983,91 @@ digraph pic { \pagehead{FiniteFieldCategory}{FFIELDC} \pagepic{ps/v102finitefieldcategory.ps}{FFIELDC}{0.70} +<>= +)set break resume +)sys rm -f FiniteFieldCategory.output +)spool FiniteFieldCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldCategory +--R FiniteFieldCategory is a category constructor +--R Abbreviation for FiniteFieldCategory is FFIELDC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FFIELDC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean charthRoot : % -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R createPrimitiveElement : () -> % differentiate : % -> % +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R index : PositiveInteger -> % init : () -> % +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R lookup : % -> PositiveInteger one? : % -> Boolean +--R order : % -> PositiveInteger prime? : % -> Boolean +--R primeFrobenius : % -> % primitive? : % -> Boolean +--R primitiveElement : () -> % ?quo? : (%,%) -> % +--R random : () -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R size : () -> NonNegativeInteger sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") +--R conditionP : Matrix % -> Union(Vector %,"failed") +--R differentiate : (%,NonNegativeInteger) -> % +--R discreteLog : % -> NonNegativeInteger +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") +--R order : % -> OnePointCompletion PositiveInteger +--R primeFrobenius : (%,NonNegativeInteger) -> % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R representationType : () -> Union("prime",polynomial,normal,cyclic) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldCategory examples +==================================================================== + +See Also: +o )show FiniteFieldCategory + +@ {\bf See:} \pagefrom{DifferentialRing}{DIFRING} @@ -57110,6 +69570,102 @@ digraph pic { \pagehead{FloatingPointSystem}{FPS} \pagepic{ps/v102floatingpointsystem.ps}{FPS}{0.50} +<>= +)set break resume +)sys rm -f FloatingPointSystem.output +)spool FloatingPointSystem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FloatingPointSystem +--R FloatingPointSystem is a category constructor +--R Abbreviation for FloatingPointSystem is FPS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FPS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R associates? : (%,%) -> Boolean base : () -> PositiveInteger +--R bits : () -> PositiveInteger ceiling : % -> % +--R coerce : Fraction Integer -> % coerce : Integer -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Pattern Float convert : % -> DoubleFloat +--R convert : % -> Float digits : () -> PositiveInteger +--R exponent : % -> Integer factor : % -> Factored % +--R float : (Integer,Integer) -> % floor : % -> % +--R fractionPart : % -> % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R mantissa : % -> Integer max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R norm : % -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean order : % -> Integer +--R positive? : % -> Boolean precision : () -> PositiveInteger +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction Integer retract : % -> Integer +--R round : % -> % sample : () -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R sqrt : % -> % squareFree : % -> Factored % +--R squareFreePart : % -> % truncate : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> Integer zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R characteristic : () -> NonNegativeInteger +--R decreasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R digits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R float : (Integer,Integer,PositiveInteger) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R max : () -> % if not has($,arbitraryPrecision) and not has($,arbitraryExponent) +--R min : () -> % if not has($,arbitraryPrecision) and not has($,arbitraryExponent) +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R precision : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FloatingPointSystem examples +==================================================================== + +See Also: +o )show FloatingPointSystem + +@ {\bf See:} \pagefrom{RealNumberSystem}{RNS} @@ -57491,6 +70047,69 @@ digraph pic { \pagehead{FramedAlgebra}{FRAMALG} \pagepic{ps/v102framedalgebra.ps}{FRAMALG}{0.50} +<>= +)set break resume +)sys rm -f FramedAlgebra.output +)spool FramedAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FramedAlgebra +--R FramedAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory t#1) is a category constructor +--R Abbreviation for FramedAlgebra is FRAMALG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FRAMALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : Vector R -> % +--R convert : % -> Vector R coordinates : % -> Vector R +--R discriminant : () -> R discriminant : Vector % -> R +--R hash : % -> SingleInteger latex : % -> String +--R norm : % -> R one? : % -> Boolean +--R rank : () -> PositiveInteger recip : % -> Union(%,"failed") +--R represents : Vector R -> % sample : () -> % +--R trace : % -> R traceMatrix : () -> Matrix R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UP +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coordinates : Vector % -> Matrix R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R minimalPolynomial : % -> UP if R has FIELD +--R regularRepresentation : % -> Matrix R +--R regularRepresentation : (%,Vector %) -> Matrix R +--R represents : (Vector R,Vector %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R traceMatrix : Vector % -> Matrix R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FramedAlgebra examples +==================================================================== + +See Also: +o )show FramedAlgebra + +@ {\bf See:} \pageto{MonogenicAlgebra}{MONOGEN} @@ -57757,6 +70376,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{PseudoAlgebraicClosureOfFiniteFieldCategory}{PACFFC} \pagepic{ps/v102pseudoalgebraicclosureoffinitefieldcategory.ps}{PACFFC}{0.50} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfFiniteFieldCategory.output @@ -58129,6 +70749,219 @@ digraph pic { \pagehead{UnivariateLaurentSeriesConstructorCategory}{ULSCCAT} \pagepic{ps/v102univariatelaurentseriesconstructorcategory.ps}{ULSCCAT}{0.50} +<>= +)set break resume +)sys rm -f UnivariateLaurentSeriesConstructorCategory.output +)spool UnivariateLaurentSeriesConstructorCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariateLaurentSeriesConstructorCategory +--R UnivariateLaurentSeriesConstructorCategory(Coef: Ring,UTS: UnivariateTaylorSeriesCategory t#1) is a category constructor +--R Abbreviation for UnivariateLaurentSeriesConstructorCategory is ULSCCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ULSCCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficient : (%,Integer) -> Coef coerce : UTS -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> Integer +--R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % +--R hash : % -> SingleInteger latex : % -> String +--R laurent : (Integer,UTS) -> % leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial : (Coef,Integer) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : (%,Integer) -> Integer +--R order : % -> Integer pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R removeZeroes : (Integer,%) -> % removeZeroes : % -> % +--R retract : % -> UTS sample : () -> % +--R taylor : % -> UTS taylorRep : % -> UTS +--R truncate : (%,Integer) -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (UTS,%) -> % if Coef has FIELD +--R ?*? : (%,UTS) -> % if Coef has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (UTS,UTS) -> % if Coef has FIELD +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R ? Boolean if and(has(UTS,OrderedSet),has(Coef,Field)) +--R ?<=? : (%,%) -> Boolean if and(has(UTS,OrderedSet),has(Coef,Field)) +--R ?>? : (%,%) -> Boolean if and(has(UTS,OrderedSet),has(Coef,Field)) +--R ?>=? : (%,%) -> Boolean if and(has(UTS,OrderedSet),has(Coef,Field)) +--R D : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : (%,List Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R D : % -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef +--R D : (%,(UTS -> UTS),NonNegativeInteger) -> % if Coef has FIELD +--R D : (%,(UTS -> UTS)) -> % if Coef has FIELD +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if and(has(UTS,OrderedIntegralDomain),has(Coef,Field)) +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R ceiling : % -> UTS if and(has(UTS,IntegerNumberSystem),has(Coef,Field)) +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if and(OR(has(UTS,CharacteristicNonZero),and(has($,CharacteristicNonZero),has(UTS,PolynomialFactorizationExplicit))),has(Coef,Field)) or Coef has CHARNZ +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : Symbol -> % if and(has(UTS,RetractableTo Symbol),has(Coef,Field)) +--R coerce : Coef -> % if Coef has COMRING +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(and(has($,CharacteristicNonZero),has(UTS,PolynomialFactorizationExplicit)),has(Coef,Field)) +--R convert : % -> Pattern Integer if and(has(UTS,ConvertibleTo Pattern Integer),has(Coef,Field)) +--R convert : % -> Pattern Float if and(has(UTS,ConvertibleTo Pattern Float),has(Coef,Field)) +--R convert : % -> InputForm if and(has(UTS,ConvertibleTo InputForm),has(Coef,Field)) +--R convert : % -> Float if and(has(UTS,RealConstant),has(Coef,Field)) +--R convert : % -> DoubleFloat if and(has(UTS,RealConstant),has(Coef,Field)) +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R denom : % -> UTS if Coef has FIELD +--R denominator : % -> % if Coef has FIELD +--R differentiate : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,List Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef +--R differentiate : % -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,(UTS -> UTS),NonNegativeInteger) -> % if Coef has FIELD +--R differentiate : (%,(UTS -> UTS)) -> % if Coef has FIELD +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,UTS) -> % if and(has(UTS,Eltable(UTS,UTS)),has(Coef,Field)) +--R ?.? : (%,%) -> % if Integer has SGROUP +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,List UTS,List UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field)) +--R eval : (%,UTS,UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field)) +--R eval : (%,Equation UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field)) +--R eval : (%,List Equation UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field)) +--R eval : (%,List Symbol,List UTS) -> % if and(has(UTS,InnerEvalable(Symbol,UTS)),has(Coef,Field)) +--R eval : (%,Symbol,UTS) -> % if and(has(UTS,InnerEvalable(Symbol,UTS)),has(Coef,Field)) +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field)) +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field)) +--R floor : % -> UTS if and(has(UTS,IntegerNumberSystem),has(Coef,Field)) +--R fractionPart : % -> % if and(has(UTS,EuclideanDomain),has(Coef,Field)) +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R init : () -> % if and(has(UTS,StepThrough),has(Coef,Field)) +--R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R map : ((UTS -> UTS),%) -> % if Coef has FIELD +--R max : (%,%) -> % if and(has(UTS,OrderedSet),has(Coef,Field)) +--R min : (%,%) -> % if and(has(UTS,OrderedSet),has(Coef,Field)) +--R monomial : (%,List SingletonAsOrderedSet,List Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R negative? : % -> Boolean if and(has(UTS,OrderedIntegralDomain),has(Coef,Field)) +--R nextItem : % -> Union(%,"failed") if and(has(UTS,StepThrough),has(Coef,Field)) +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R numer : % -> UTS if Coef has FIELD +--R numerator : % -> % if Coef has FIELD +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if and(has(UTS,PatternMatchable Integer),has(Coef,Field)) +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if and(has(UTS,PatternMatchable Float),has(Coef,Field)) +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R positive? : % -> Boolean if and(has(UTS,OrderedIntegralDomain),has(Coef,Field)) +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R ?quo? : (%,%) -> % if Coef has FIELD +--R random : () -> % if and(has(UTS,IntegerNumberSystem),has(Coef,Field)) +--R rationalFunction : (%,Integer,Integer) -> Fraction Polynomial Coef if Coef has INTDOM +--R rationalFunction : (%,Integer) -> Fraction Polynomial Coef if Coef has INTDOM +--R reducedSystem : Matrix % -> Matrix Integer if and(has(UTS,LinearlyExplicitRingOver Integer),has(Coef,Field)) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(UTS,LinearlyExplicitRingOver Integer),has(Coef,Field)) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix UTS,vec: Vector UTS) if Coef has FIELD +--R reducedSystem : Matrix % -> Matrix UTS if Coef has FIELD +--R ?rem? : (%,%) -> % if Coef has FIELD +--R retract : % -> Symbol if and(has(UTS,RetractableTo Symbol),has(Coef,Field)) +--R retract : % -> Fraction Integer if and(has(UTS,RetractableTo Integer),has(Coef,Field)) +--R retract : % -> Integer if and(has(UTS,RetractableTo Integer),has(Coef,Field)) +--R retractIfCan : % -> Union(Symbol,"failed") if and(has(UTS,RetractableTo Symbol),has(Coef,Field)) +--R retractIfCan : % -> Union(Fraction Integer,"failed") if and(has(UTS,RetractableTo Integer),has(Coef,Field)) +--R retractIfCan : % -> Union(Integer,"failed") if and(has(UTS,RetractableTo Integer),has(Coef,Field)) +--R retractIfCan : % -> Union(UTS,"failed") +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : Stream Record(k: Integer,c: Coef) -> % +--R sign : % -> Integer if and(has(UTS,OrderedIntegralDomain),has(Coef,Field)) +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field)) +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field)) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R taylorIfCan : % -> Union(UTS,"failed") +--R terms : % -> Stream Record(k: Integer,c: Coef) +--R truncate : (%,Integer,Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R wholePart : % -> UTS if and(has(UTS,EuclideanDomain),has(Coef,Field)) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariateLaurentSeriesConstructorCategory examples +==================================================================== + +See Also: +o )show UnivariateLaurentSeriesConstructorCategory + +@ {\bf See:} \pagefrom{RetractableTo}{RETRACT} @@ -58783,6 +71616,162 @@ digraph pic { \pagehead{UnivariatePuiseuxSeriesConstructorCategory}{UPXSCCA} \pagepic{ps/v102univariatepuiseuxseriesconstructorcategory.ps}{UPXSCCA}{0.50} +<>= +)set break resume +)sys rm -f UnivariatePuiseuxSeriesConstructorCategory.output +)spool UnivariatePuiseuxSeriesConstructorCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariatePuiseuxSeriesConstructorCategory +--R UnivariatePuiseuxSeriesConstructorCategory(Coef: Ring,ULS: UnivariateLaurentSeriesCategory t#1) is a category constructor +--R Abbreviation for UnivariatePuiseuxSeriesConstructorCategory is UPXSCCA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPXSCCA +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coerce : ULS -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Fraction Integer hash : % -> SingleInteger +--R latex : % -> String laurent : % -> ULS +--R laurentRep : % -> ULS leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> Fraction Integer pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> ULS sample : () -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,Fraction Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,%) -> % if Fraction Integer has SGROUP +--R ?.? : (%,Fraction Integer) -> Coef +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,Fraction Integer) -> % +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R laurentIfCan : % -> Union(ULS,"failed") +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % +--R monomial : (Coef,Fraction Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyExponents : (%,Fraction Integer) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,Fraction Integer) -> Fraction Integer +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R puiseux : (Fraction Integer,ULS) -> % +--R ?quo? : (%,%) -> % if Coef has FIELD +--R rationalPower : % -> Fraction Integer +--R ?rem? : (%,%) -> % if Coef has FIELD +--R retractIfCan : % -> Union(ULS,"failed") +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: Fraction Integer,c: Coef) +--R truncate : (%,Fraction Integer,Fraction Integer) -> % +--R truncate : (%,Fraction Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariatePuiseuxSeriesConstructorCategory examples +==================================================================== + +See Also: +o )show UnivariatePuiseuxSeriesConstructorCategory + +@ {\bf See:} \pagefrom{RetractableTo}{RETRACT} @@ -59248,6 +72237,127 @@ digraph pic { \pagehead{FiniteAlgebraicExtensionField}{FAXF} \pagepic{ps/v102finitealgebraicextensionfield.ps}{FAXF}{0.75} +<>= +)set break resume +)sys rm -f FiniteAlgebraicExtensionField.output +)spool FiniteAlgebraicExtensionField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteAlgebraicExtensionField +--R FiniteAlgebraicExtensionField F: Field is a category constructor +--R Abbreviation for FiniteAlgebraicExtensionField is FAXF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FAXF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (F,%) -> % ?*? : (%,F) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,F) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if F has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : F -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector F degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> F one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector F -> % retract : % -> F +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> F transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if F has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if F has FINITE +--R Frobenius : % -> % if F has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if F has CHARNZ or F has FINITE +--R charthRoot : % -> % if F has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if F has FINITE +--R coordinates : Vector % -> Matrix F +--R createNormalElement : () -> % if F has FINITE +--R createPrimitiveElement : () -> % if F has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial F +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if F has FINITE +--R differentiate : % -> % if F has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if F has CHARNZ or F has FINITE +--R discreteLog : % -> NonNegativeInteger if F has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if F has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if F has FINITE +--R index : PositiveInteger -> % if F has FINITE +--R init : () -> % if F has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial F) -> % if F has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial F,"failed") if F has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial F if F has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial F if F has FINITE +--R lookup : % -> PositiveInteger if F has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if F has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial F +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if F has FINITE +--R norm : (%,PositiveInteger) -> % if F has FINITE +--R normal? : % -> Boolean if F has FINITE +--R normalElement : () -> % if F has FINITE +--R order : % -> OnePointCompletion PositiveInteger if F has CHARNZ or F has FINITE +--R order : % -> PositiveInteger if F has FINITE +--R primeFrobenius : % -> % if F has CHARNZ or F has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if F has CHARNZ or F has FINITE +--R primitive? : % -> Boolean if F has FINITE +--R primitiveElement : () -> % if F has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if F has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if F has FINITE +--R retractIfCan : % -> Union(F,"failed") +--R size : () -> NonNegativeInteger if F has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if F has FINITE +--R trace : (%,PositiveInteger) -> % if F has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteAlgebraicExtensionField examples +==================================================================== + +See Also: +o )show FiniteAlgebraicExtensionField + +@ {\bf See:} \pagefrom{ExtensionField}{XF} @@ -59896,6 +73006,151 @@ digraph pic { \pagehead{MonogenicAlgebra}{MONOGEN} \pagepic{ps/v102monogenicalgebra.ps}{MONOGEN}{0.40} +<>= +)set break resume +)sys rm -f MonogenicAlgebra.output +)spool MonogenicAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MonogenicAlgebra +--R MonogenicAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory t#1) is a category constructor +--R Abbreviation for MonogenicAlgebra is MONOGEN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONOGEN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : UP -> % +--R convert : % -> UP convert : Vector R -> % +--R convert : % -> Vector R coordinates : % -> Vector R +--R definingPolynomial : () -> UP discriminant : () -> R +--R discriminant : Vector % -> R generator : () -> % +--R hash : % -> SingleInteger inv : % -> % if R has FIELD +--R latex : % -> String lift : % -> UP +--R norm : % -> R one? : % -> Boolean +--R rank : () -> PositiveInteger recip : % -> Union(%,"failed") +--R reduce : UP -> % represents : Vector R -> % +--R retract : % -> R sample : () -> % +--R trace : % -> R traceMatrix : () -> Matrix R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has FIELD +--R ?*? : (Fraction Integer,%) -> % if R has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if R has FIELD +--R D : (%,(R -> R)) -> % if R has FIELD +--R D : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD +--R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R D : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R D : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R D : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC +--R D : % -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC +--R ?^? : (%,Integer) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has FIELD +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UP +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R charthRoot : % -> % if R has FFIELDC +--R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT +--R coerce : % -> % if R has FIELD +--R conditionP : Matrix % -> Union(Vector %,"failed") if R has FFIELDC +--R coordinates : Vector % -> Matrix R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R createPrimitiveElement : () -> % if R has FFIELDC +--R derivationCoordinates : (Vector %,(R -> R)) -> Matrix R if R has FIELD +--R differentiate : (%,(R -> R)) -> % if R has FIELD +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R differentiate : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R differentiate : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field)) +--R differentiate : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC +--R differentiate : % -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC +--R discreteLog : % -> NonNegativeInteger if R has FFIELDC +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has FIELD +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if R has FFIELDC +--R gcd : (%,%) -> % if R has FIELD +--R gcd : List % -> % if R has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD +--R index : PositiveInteger -> % if R has FINITE +--R init : () -> % if R has FFIELDC +--R lcm : (%,%) -> % if R has FIELD +--R lcm : List % -> % if R has FIELD +--R lookup : % -> PositiveInteger if R has FINITE +--R minimalPolynomial : % -> UP if R has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R nextItem : % -> Union(%,"failed") if R has FFIELDC +--R order : % -> OnePointCompletion PositiveInteger if R has FFIELDC +--R order : % -> PositiveInteger if R has FFIELDC +--R prime? : % -> Boolean if R has FIELD +--R primeFrobenius : % -> % if R has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if R has FFIELDC +--R primitive? : % -> Boolean if R has FFIELDC +--R primitiveElement : () -> % if R has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R ?quo? : (%,%) -> % if R has FIELD +--R random : () -> % if R has FINITE +--R reduce : Fraction UP -> Union(%,"failed") if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R regularRepresentation : % -> Matrix R +--R regularRepresentation : (%,Vector %) -> Matrix R +--R ?rem? : (%,%) -> % if R has FIELD +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC +--R represents : (Vector R,Vector %) -> % +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R size : () -> NonNegativeInteger if R has FINITE +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R squareFree : % -> Factored % if R has FIELD +--R squareFreePart : % -> % if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC +--R traceMatrix : Vector % -> Matrix R +--R unit? : % -> Boolean if R has FIELD +--R unitCanonical : % -> % if R has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MonogenicAlgebra examples +==================================================================== + +See Also: +o )show MonogenicAlgebra + +@ {\bf See:} \pageto{FunctionFieldCategory}{FFCAT} @@ -60391,6 +73646,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{PseudoAlgebraicClosureOfRationalNumberCategory}{PACRATC} \pagepic{ps/v102pseudoalgebraicclosureofrationalnumbercategory.ps}{PACRATC}{0.50} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfRationalNumberCategory.output @@ -60770,6 +74026,217 @@ digraph pic { \pagehead{ComplexCategory}{COMPCAT} \pagepic{ps/v102complexcategory.ps}{COMPCAT}{0.50} +<>= +)set break resume +)sys rm -f ComplexCategory.output +)spool ComplexCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ComplexCategory +--R ComplexCategory R: CommutativeRing is a category constructor +--R Abbreviation for ComplexCategory is COMPCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for COMPCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if R has RNS basis : () -> Vector % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm complex : (R,R) -> % +--R conjugate : % -> % convert : Vector R -> % +--R convert : % -> Vector R coordinates : % -> Vector R +--R discriminant : () -> R discriminant : Vector % -> R +--R generator : () -> % hash : % -> SingleInteger +--R imag : % -> R imaginary : () -> % +--R inv : % -> % if R has FIELD latex : % -> String +--R map : ((R -> R),%) -> % norm : % -> R +--R one? : % -> Boolean pi : () -> % if R has TRANFUN +--R rank : () -> PositiveInteger real : % -> R +--R recip : % -> Union(%,"failed") represents : Vector R -> % +--R retract : % -> R sample : () -> % +--R trace : % -> R traceMatrix : () -> Matrix R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has FIELD +--R ?*? : (Fraction Integer,%) -> % if R has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,%) -> % if R has TRANFUN +--R ?**? : (%,Fraction Integer) -> % if R has RADCAT and R has TRANFUN +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : % -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field)) +--R D : (%,NonNegativeInteger) -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field)) +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if R has TRANFUN +--R acosh : % -> % if R has TRANFUN +--R acot : % -> % if R has TRANFUN +--R acoth : % -> % if R has TRANFUN +--R acsc : % -> % if R has TRANFUN +--R acsch : % -> % if R has TRANFUN +--R argument : % -> R if R has TRANFUN +--R asec : % -> % if R has TRANFUN +--R asech : % -> % if R has TRANFUN +--R asin : % -> % if R has TRANFUN +--R asinh : % -> % if R has TRANFUN +--R associates? : (%,%) -> Boolean if R has INTDOM or R has EUCDOM and R has PFECAT +--R atan : % -> % if R has TRANFUN +--R atanh : % -> % if R has TRANFUN +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> SparseUnivariatePolynomial R +--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),AND(has(R,EuclideanDomain),has(R,PolynomialFactorizationExplicit))) or R has CHARNZ +--R charthRoot : % -> % if R has FFIELDC +--R coerce : % -> % if R has INTDOM or R has EUCDOM and R has PFECAT +--R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT +--R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),AND(has(R,EuclideanDomain),has(R,PolynomialFactorizationExplicit))) or R has FFIELDC +--R convert : % -> InputForm if R has KONVERT INFORM +--R convert : % -> Complex DoubleFloat if R has REAL +--R convert : % -> Complex Float if R has REAL +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT +--R convert : SparseUnivariatePolynomial R -> % +--R convert : % -> SparseUnivariatePolynomial R +--R coordinates : Vector % -> Matrix R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R cos : % -> % if R has TRANFUN +--R cosh : % -> % if R has TRANFUN +--R cot : % -> % if R has TRANFUN +--R coth : % -> % if R has TRANFUN +--R createPrimitiveElement : () -> % if R has FFIELDC +--R csc : % -> % if R has TRANFUN +--R csch : % -> % if R has TRANFUN +--R definingPolynomial : () -> SparseUnivariatePolynomial R +--R derivationCoordinates : (Vector %,(R -> R)) -> Matrix R if R has FIELD +--R differentiate : % -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field)) +--R differentiate : (%,NonNegativeInteger) -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field)) +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC +--R discreteLog : % -> NonNegativeInteger if R has FFIELDC +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has EUCDOM +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R euclideanSize : % -> NonNegativeInteger if R has EUCDOM +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List Equation R) -> % if R has EVALAB R +--R eval : (%,Equation R) -> % if R has EVALAB R +--R eval : (%,R,R) -> % if R has EVALAB R +--R eval : (%,List R,List R) -> % if R has EVALAB R +--R exp : % -> % if R has TRANFUN +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has EUCDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM or R has EUCDOM and R has PFECAT +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has EUCDOM +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has EUCDOM +--R factor : % -> Factored % if R has EUCDOM and R has PFECAT or R has FIELD +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has EUCDOM and R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has EUCDOM and R has PFECAT +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if R has FFIELDC +--R gcd : (%,%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT +--R gcd : List % -> % if R has EUCDOM or R has EUCDOM and R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has EUCDOM or R has EUCDOM and R has PFECAT +--R index : PositiveInteger -> % if R has FINITE +--R init : () -> % if R has FFIELDC +--R lcm : (%,%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT +--R lcm : List % -> % if R has EUCDOM or R has EUCDOM and R has PFECAT +--R lift : % -> SparseUnivariatePolynomial R +--R log : % -> % if R has TRANFUN +--R lookup : % -> PositiveInteger if R has FINITE +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimalPolynomial : % -> SparseUnivariatePolynomial R if R has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has EUCDOM +--R nextItem : % -> Union(%,"failed") if R has FFIELDC +--R nthRoot : (%,Integer) -> % if R has RADCAT and R has TRANFUN +--R order : % -> OnePointCompletion PositiveInteger if R has FFIELDC +--R order : % -> PositiveInteger if R has FFIELDC +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT +--R polarCoordinates : % -> Record(r: R,phi: R) if R has RNS and R has TRANFUN +--R prime? : % -> Boolean if R has EUCDOM and R has PFECAT or R has FIELD +--R primeFrobenius : % -> % if R has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if R has FFIELDC +--R primitive? : % -> Boolean if R has FFIELDC +--R primitiveElement : () -> % if R has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has EUCDOM +--R ?quo? : (%,%) -> % if R has EUCDOM +--R random : () -> % if R has FINITE +--R rational : % -> Fraction Integer if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R reduce : Fraction SparseUnivariatePolynomial R -> Union(%,"failed") if R has FIELD +--R reduce : SparseUnivariatePolynomial R -> % +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R regularRepresentation : % -> Matrix R +--R regularRepresentation : (%,Vector %) -> Matrix R +--R ?rem? : (%,%) -> % if R has EUCDOM +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC +--R represents : (Vector R,Vector %) -> % +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R sec : % -> % if R has TRANFUN +--R sech : % -> % if R has TRANFUN +--R sin : % -> % if R has TRANFUN +--R sinh : % -> % if R has TRANFUN +--R size : () -> NonNegativeInteger if R has FINITE +--R sizeLess? : (%,%) -> Boolean if R has EUCDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has EUCDOM and R has PFECAT +--R sqrt : % -> % if R has RADCAT and R has TRANFUN +--R squareFree : % -> Factored % if R has EUCDOM and R has PFECAT or R has FIELD +--R squareFreePart : % -> % if R has EUCDOM and R has PFECAT or R has FIELD +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has EUCDOM and R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC +--R tan : % -> % if R has TRANFUN +--R tanh : % -> % if R has TRANFUN +--R traceMatrix : Vector % -> Matrix R +--R unit? : % -> Boolean if R has INTDOM or R has EUCDOM and R has PFECAT +--R unitCanonical : % -> % if R has INTDOM or R has EUCDOM and R has PFECAT +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM or R has EUCDOM and R has PFECAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ComplexCategory examples +==================================================================== + +See Also: +o )show ComplexCategory + +@ {\bf See:} \pagefrom{CommutativeRing}{COMRING} @@ -61707,6 +75174,185 @@ digraph pic { \pagehead{FunctionFieldCategory}{FFCAT} \pagepic{ps/v102functionfieldcategory.ps}{FFCAT}{0.70} +<>= +)set break resume +)sys rm -f FunctionFieldCategory.output +)spool FunctionFieldCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FunctionFieldCategory +--R FunctionFieldCategory(F: UniqueFactorizationDomain,UP: UnivariatePolynomialCategory t#1,UPUP: UnivariatePolynomialCategory Fraction t#2) is a category constructor +--R Abbreviation for FunctionFieldCategory is FFCAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FFCAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction UP,%) -> % ?*? : (%,Fraction UP) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean +--R coerce : Fraction UP -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : UPUP -> % +--R convert : % -> UPUP convert : Vector Fraction UP -> % +--R convert : % -> Vector Fraction UP definingPolynomial : () -> UPUP +--R discriminant : () -> Fraction UP elt : (%,F,F) -> F +--R generator : () -> % genus : () -> NonNegativeInteger +--R hash : % -> SingleInteger integral? : (%,UP) -> Boolean +--R integral? : (%,F) -> Boolean integral? : % -> Boolean +--R integralBasis : () -> Vector % latex : % -> String +--R lift : % -> UPUP norm : % -> Fraction UP +--R one? : % -> Boolean primitivePart : % -> % +--R ramified? : UP -> Boolean ramified? : F -> Boolean +--R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean +--R recip : % -> Union(%,"failed") reduce : UPUP -> % +--R represents : (Vector UP,UP) -> % retract : % -> Fraction UP +--R sample : () -> % singular? : UP -> Boolean +--R singular? : F -> Boolean trace : % -> Fraction UP +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Fraction UP has FIELD +--R ?*? : (Fraction Integer,%) -> % if Fraction UP has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if Fraction UP has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Fraction UP has FIELD +--R D : % -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC +--R D : (%,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC +--R D : (%,Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R D : (%,List Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R D : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD +--R D : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD +--R ?^? : (%,Integer) -> % if Fraction UP has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R absolutelyIrreducible? : () -> Boolean +--R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) +--R associates? : (%,%) -> Boolean if Fraction UP has FIELD +--R branchPointAtInfinity? : () -> Boolean +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UPUP +--R charthRoot : % -> Union(%,"failed") if Fraction UP has CHARNZ +--R charthRoot : % -> % if Fraction UP has FFIELDC +--R coerce : % -> % if Fraction UP has FIELD +--R coerce : Fraction Integer -> % if Fraction UP has FIELD or Fraction UP has RETRACT FRAC INT +--R complementaryBasis : Vector % -> Vector % +--R conditionP : Matrix % -> Union(Vector %,"failed") if Fraction UP has FFIELDC +--R coordinates : Vector % -> Matrix Fraction UP +--R coordinates : % -> Vector Fraction UP +--R coordinates : (Vector %,Vector %) -> Matrix Fraction UP +--R coordinates : (%,Vector %) -> Vector Fraction UP +--R createPrimitiveElement : () -> % if Fraction UP has FFIELDC +--R derivationCoordinates : (Vector %,(Fraction UP -> Fraction UP)) -> Matrix Fraction UP if Fraction UP has FIELD +--R differentiate : % -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC +--R differentiate : (%,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC +--R differentiate : (%,Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R differentiate : (%,List Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field)) +--R differentiate : (%,(UP -> UP)) -> % +--R differentiate : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD +--R differentiate : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction UP has FFIELDC +--R discreteLog : % -> NonNegativeInteger if Fraction UP has FFIELDC +--R discriminant : Vector % -> Fraction UP +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction UP has FIELD +--R elliptic : () -> Union(UP,"failed") +--R euclideanSize : % -> NonNegativeInteger if Fraction UP has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Fraction UP has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction UP has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction UP has FIELD +--R factor : % -> Factored % if Fraction UP has FIELD +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if Fraction UP has FFIELDC +--R gcd : (%,%) -> % if Fraction UP has FIELD +--R gcd : List % -> % if Fraction UP has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Fraction UP has FIELD +--R hyperelliptic : () -> Union(UP,"failed") +--R index : PositiveInteger -> % if Fraction UP has FINITE +--R init : () -> % if Fraction UP has FFIELDC +--R integralAtInfinity? : % -> Boolean +--R integralBasisAtInfinity : () -> Vector % +--R integralCoordinates : % -> Record(num: Vector UP,den: UP) +--R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix UP,den: UP) +--R integralMatrix : () -> Matrix Fraction UP +--R integralMatrixAtInfinity : () -> Matrix Fraction UP +--R integralRepresents : (Vector UP,UP) -> % +--R inv : % -> % if Fraction UP has FIELD +--R inverseIntegralMatrix : () -> Matrix Fraction UP +--R inverseIntegralMatrixAtInfinity : () -> Matrix Fraction UP +--R lcm : (%,%) -> % if Fraction UP has FIELD +--R lcm : List % -> % if Fraction UP has FIELD +--R lookup : % -> PositiveInteger if Fraction UP has FINITE +--R minimalPolynomial : % -> UPUP if Fraction UP has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD +--R nextItem : % -> Union(%,"failed") if Fraction UP has FFIELDC +--R nonSingularModel : Symbol -> List Polynomial F if F has FIELD +--R normalizeAtInfinity : Vector % -> Vector % +--R numberOfComponents : () -> NonNegativeInteger +--R order : % -> OnePointCompletion PositiveInteger if Fraction UP has FFIELDC +--R order : % -> PositiveInteger if Fraction UP has FFIELDC +--R prime? : % -> Boolean if Fraction UP has FIELD +--R primeFrobenius : % -> % if Fraction UP has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction UP has FFIELDC +--R primitive? : % -> Boolean if Fraction UP has FFIELDC +--R primitiveElement : () -> % if Fraction UP has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Fraction UP has FIELD +--R ?quo? : (%,%) -> % if Fraction UP has FIELD +--R ramifiedAtInfinity? : () -> Boolean +--R random : () -> % if Fraction UP has FINITE +--R rationalPoints : () -> List List F if F has FINITE +--R reduce : Fraction UPUP -> Union(%,"failed") if Fraction UP has FIELD +--R reduceBasisAtInfinity : Vector % -> Vector % +--R reducedSystem : Matrix % -> Matrix Fraction UP +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction UP,vec: Vector Fraction UP) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if Fraction UP has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if Fraction UP has LINEXP INT +--R regularRepresentation : % -> Matrix Fraction UP +--R regularRepresentation : (%,Vector %) -> Matrix Fraction UP +--R ?rem? : (%,%) -> % if Fraction UP has FIELD +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction UP has FFIELDC +--R represents : Vector Fraction UP -> % +--R represents : (Vector Fraction UP,Vector %) -> % +--R retract : % -> Fraction Integer if Fraction UP has RETRACT FRAC INT +--R retract : % -> Integer if Fraction UP has RETRACT INT +--R retractIfCan : % -> Union(Fraction UP,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction UP has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if Fraction UP has RETRACT INT +--R singularAtInfinity? : () -> Boolean +--R size : () -> NonNegativeInteger if Fraction UP has FINITE +--R sizeLess? : (%,%) -> Boolean if Fraction UP has FIELD +--R squareFree : % -> Factored % if Fraction UP has FIELD +--R squareFreePart : % -> % if Fraction UP has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction UP has FFIELDC +--R traceMatrix : () -> Matrix Fraction UP +--R traceMatrix : Vector % -> Matrix Fraction UP +--R unit? : % -> Boolean if Fraction UP has FIELD +--R unitCanonical : % -> % if Fraction UP has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction UP has FIELD +--R yCoordinates : % -> Record(num: Vector UP,den: UP) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FunctionFieldCategory examples +==================================================================== + +See Also: +o )show FunctionFieldCategory + +@ {\bf See:} \pagefrom{MonogenicAlgebra}{MONOGEN} @@ -62691,6 +76337,7 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory}{PACEXTC} \pagepic{ps/v102pseudoalgebraicclosureofalgextofrationalnumbercategory.ps}{PACEXTC}{0.50} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory.output diff --git a/changelog b/changelog index ae90180..5d7ce6f 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100529 tpd src/axiom-website/patches.html 20100529.04.tpd.patch +20100529 tpd src/algebra/Makefile add test and help files for all categories +20100529 tpd books/bookvol10.2 add test and help files for all categories 20100529 tpd src/axiom-website/patches.html 20100529.03.tpd.patch 20100529 tpd books/bookvolbib AL94 Adams, William W. and Loustaunau, Philippe 20100529 tpd src/axiom-website/patches.html 20100529.02.tpd.patch diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 25137cb..5914c28 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -16884,7 +16884,7 @@ ${MID}/BLHN.nrlib/code.o: ${MID}/BLHN.spad @ <>= -PRSPCATDEPS = SETCATD +PRSPCATDEPS = SETCATD UTSZ ${MID}/PRSPCAT.nrlib/code.o: ${MID}/PRSPCAT.spad @echo P3 making ${MID}/PRSPCAT.nrlib/code.o from ${MID}/PRSPCAT.spad @@ -18046,99 +18046,200 @@ This keeps the regression test list in the algebra Makefile. HELPFILE=${HELP}/help.help SPADHELP=\ + ${HELP}/AbelianGroup.help \ + ${HELP}/AbelianMonoid.help \ + ${HELP}/AbelianMonoidRing.help \ + ${HELP}/AbelianSemiGroup.help \ ${HELP}/AffineAlgebraicSetComputeWithGroebnerBasis.help \ ${HELP}/AffineAlgebraicSetComputeWithResultant.help \ ${HELP}/AffinePlane.help \ ${HELP}/AffinePlaneOverPseudoAlgebraicClosureOfFiniteField.help \ ${HELP}/AffineSpace.help \ ${HELP}/AffineSpaceCategory.help \ + ${HELP}/Aggregate.help \ + ${HELP}/Algebra.help \ ${HELP}/AlgebraicallyClosedField.help \ + ${HELP}/AlgebraicallyClosedFunctionSpace.help \ ${HELP}/Any.help \ ${HELP}/ApplicationProgramInterface.help \ + ${HELP}/ArcHyperbolicFunctionCategory.help \ + ${HELP}/ArcTrigonometricFunctionCategory.help \ ${HELP}/ArrayStack.help \ ${HELP}/AssociationList.help \ + ${HELP}/AssociationListAggregate.help \ ${HELP}/BalancedBinaryTree.help \ + ${HELP}/BagAggregate.help \ ${HELP}/BasicOperator.help \ + ${HELP}/BasicType.help \ ${HELP}/Bezier.help \ + ${HELP}/BiModule.help \ ${HELP}/BinaryExpansion.help \ + ${HELP}/BinaryRecursiveAggregate.help \ ${HELP}/BinarySearchTree.help \ + ${HELP}/BinaryTreeCategory.help \ + ${HELP}/BitAggregate.help \ ${HELP}/BlasLevelOne.help \ ${HELP}/BlowUpMethodCategory.help \ ${HELP}/BlowUpPackage.help \ ${HELP}/BlowUpWithHamburgerNoether.help \ ${HELP}/BlowUpWithQuadTrans.help \ + ${HELP}/CachableSet.help \ + ${HELP}/CancellationAbelianMonoid.help \ ${HELP}/CardinalNumber.help \ ${HELP}/CartesianTensor.help \ ${HELP}/Character.help \ ${HELP}/CharacterClass.help \ + ${HELP}/CharacteristicNonZero.help \ + ${HELP}/CharacteristicZero.help \ ${HELP}/CliffordAlgebra.help \ + ${HELP}/CoercibleTo.help \ + ${HELP}/Collection.help \ ${HELP}/CombinatorialFunction.help \ + ${HELP}/CombinatorialFunctionCategory.help \ + ${HELP}/CombinatorialOpsCategory.help \ + ${HELP}/CommutativeRing.help \ ${HELP}/Complex.help \ + ${HELP}/ComplexCategory.help \ ${HELP}/ContinuedFraction.help \ + ${HELP}/ConvertibleTo.help \ ${HELP}/CycleIndicators.help \ ${HELP}/DecimalExpansion.help \ ${HELP}/Dequeue.help \ + ${HELP}/DequeueAggregate.help \ ${HELP}/DeRhamComplex.help \ ${HELP}/DesingTree.help \ ${HELP}/DesingTreeCategory.help \ ${HELP}/DesingTreePackage.help \ + ${HELP}/Dictionary.help \ + ${HELP}/DictionaryOperations.help \ + ${HELP}/DifferentialExtension.help \ + ${HELP}/DifferentialPolynomialCategory.help \ + ${HELP}/DifferentialRing.help \ + ${HELP}/DifferentialVariableCategory.help \ + ${HELP}/DirectProductCategory.help \ ${HELP}/DistributedMultivariatePolynomial.help \ + ${HELP}/DivisionRing.help \ ${HELP}/Divisor.help \ ${HELP}/DivisorCategory.help \ ${HELP}/DoubleFloat.help \ + ${HELP}/DoublyLinkedAggregate.help \ ${HELP}/ElementaryFunction.help \ + ${HELP}/ElementaryFunctionCategory.help \ + ${HELP}/Eltable.help \ + ${HELP}/EltableAggregate.help \ + ${HELP}/EntireRing.help \ ${HELP}/EqTable.help \ ${HELP}/Equation.help \ - ${HELP}/Expression.help \ + ${HELP}/EuclideanDomain.help \ ${HELP}/EuclideanGroebnerBasisPackage.help \ + ${HELP}/Evalable.help \ + ${HELP}/Expression.help \ + ${HELP}/ExpressionSpace.help \ + ${HELP}/ExtensibleLinearAggregate.help \ + ${HELP}/ExtensionField.help \ ${HELP}/Factored.help \ ${HELP}/FactoredFunctions2.help \ ${HELP}/FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber.help \ ${HELP}/FactorisationOverPseudoAlgebraicClosureOfRationalNumber.help \ + ${HELP}/Field.help \ + ${HELP}/FieldOfPrimeCharacteristic.help \ ${HELP}/File.help \ + ${HELP}/FileCategory.help \ ${HELP}/FileName.help \ + ${HELP}/FileNameCategory.help \ + ${HELP}/Finite.help \ + ${HELP}/FiniteAbelianMonoidRing.help \ + ${HELP}/FiniteAlgebraicExtensionField.help \ + ${HELP}/FiniteDivisorCategory.help \ + ${HELP}/FiniteFieldCategory.help \ ${HELP}/FiniteFieldFactorizationWithSizeParseBySideEffect.help \ ${HELP}/FiniteFieldSquareFreeDecomposition.help \ + ${HELP}/FiniteLinearAggregate.help \ + ${HELP}/FiniteRankAlgebra.help \ + ${HELP}/FiniteRankNonAssociativeAlgebra.help \ + ${HELP}/FiniteSetAggregate.help \ ${HELP}/FlexibleArray.help \ ${HELP}/Float.help \ + ${HELP}/FloatingPointSystem.help \ + ${HELP}/FortranFunctionCategory.help \ + ${HELP}/FortranMachineTypeCategory.help \ + ${HELP}/FortranMatrixCategory.help \ + ${HELP}/FortranMatrixFunctionCategory.help \ + ${HELP}/FortranProgramCategory.help \ + ${HELP}/FortranVectorCategory.help \ + ${HELP}/FortranVectorFunctionCategory.help \ ${HELP}/Fraction.help \ + ${HELP}/FramedAlgebra.help \ + ${HELP}/FramedNonAssociativeAlgebra.help \ + ${HELP}/FreeAbelianMonoidCategory.help \ + ${HELP}/FreeLieAlgebra.help \ + ${HELP}/FreeModuleCat.help \ ${HELP}/FullPartialFractionExpansion.help \ + ${HELP}/FullyEvalableOver.help \ + ${HELP}/FullyLinearlyExplicitRingOver.help \ + ${HELP}/FullyPatternMatchable.help \ + ${HELP}/FullyRetractableTo.help \ + ${HELP}/FunctionFieldCategory.help \ + ${HELP}/FunctionSpace.help \ + ${HELP}/GcdDomain.help \ ${HELP}/GeneralDistributedMultivariatePolynomial.help \ ${HELP}/GeneralPackageForAlgebraicFunctionField.help \ ${HELP}/GeneralSparseTable.help \ + ${HELP}/GradedAlgebra.help \ + ${HELP}/GradedModule.help \ ${HELP}/GroebnerFactorizationPackage.help \ ${HELP}/GroebnerPackage.help \ + ${HELP}/Group.help \ ${HELP}/Heap.help \ ${HELP}/HexadecimalExpansion.help \ + ${HELP}/HomogeneousAggregate.help \ ${HELP}/HomogeneousDistributedMultivariatePolynomial.help \ + ${HELP}/HyperbolicFunctionCategory.help \ + ${HELP}/IndexedAggregate.help \ ${HELP}/IndexedBits.help \ + ${HELP}/IndexedDirectProductCategory.help \ ${HELP}/InfClsPt.help \ ${HELP}/InfinitlyClosePoint.help \ ${HELP}/InfinitlyClosePointCategory.help \ ${HELP}/InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField.help \ + ${HELP}/InnerEvalable.help \ ${HELP}/Integer.help \ ${HELP}/IntegerCombinatoricFunctions.help \ ${HELP}/IntegerLinearDependence.help \ + ${HELP}/IntegerNumberSystem.help \ ${HELP}/IntegerNumberTheoryFunctions.help \ + ${HELP}/IntegralDomain.help \ ${HELP}/InterfaceGroebnerPackage.help \ ${HELP}/InterpolateFormsPackage.help \ ${HELP}/IntersectionDivisorPackage.help \ ${HELP}/Interval.help \ + ${HELP}/IntervalCategory.help \ ${HELP}/Kernel.help \ ${HELP}/KeyedAccessFile.help \ + ${HELP}/KeyedDictionary.help \ + ${HELP}/LazyStreamAggregate.help \ ${HELP}/LazardSetSolvingPackage.help \ + ${HELP}/LeftAlgebra.help \ + ${HELP}/LeftModule.help \ ${HELP}/LexTriangularPackage.help \ ${HELP}/Library.help \ + ${HELP}/LieAlgebra.help \ ${HELP}/LieExponentials.help \ ${HELP}/LiePolynomial.help \ + ${HELP}/LinearlyExplicitRingOver.help \ + ${HELP}/LinearAggregate.help \ ${HELP}/LinearOrdinaryDifferentialOperator.help \ ${HELP}/LinearOrdinaryDifferentialOperator1.help \ ${HELP}/LinearOrdinaryDifferentialOperator2.help \ + ${HELP}/LinearOrdinaryDifferentialOperatorCategory.help \ ${HELP}/LinearSystemFromPowerSeriesPackage.help \ + ${HELP}/ListAggregate.help \ + ${HELP}/LiouvillianFunctionCategory.help \ ${HELP}/List.help \ ${HELP}/LinesOpPack.help \ ${HELP}/LocalParametrizationOfSimplePointPackage.help \ ${HELP}/LocalPowerSeriesCategory.help \ + ${HELP}/Logic.help \ ${HELP}/LyndonWord.help \ ${HELP}/Magma.help \ ${HELP}/MakeFunction.help \ @@ -18148,8 +18249,17 @@ SPADHELP=\ ${HELP}/MappingPackage3.help \ ${HELP}/Matrix.help \ ${HELP}/MatrixCategory.help \ + ${HELP}/Module.help \ + ${HELP}/Monad.help \ + ${HELP}/MonadWithUnit.help \ + ${HELP}/MonogenicAlgebra.help \ + ${HELP}/MonogenicLinearOperator.help \ + ${HELP}/Monoid.help \ + ${HELP}/MultiDictionary.help \ ${HELP}/Multiset.help \ + ${HELP}/MultisetAggregate.help \ ${HELP}/MultivariatePolynomial.help \ + ${HELP}/MultivariateTaylorSeriesCategory.help \ ${HELP}/NagEigenPackage.help \ ${HELP}/NagFittingPackage.help \ ${HELP}/NagLinearEquationSolvingPackage.help \ @@ -18166,30 +18276,68 @@ SPADHELP=\ ${HELP}/NagSpecialFunctionsPackage.help \ ${HELP}/NeitherSparseOrDensePowerSeries.help \ ${HELP}/NewtonPolygon.help \ + ${HELP}/NonAssociativeAlgebra.help \ + ${HELP}/NonAssociativeRing.help \ + ${HELP}/NonAssociativeRng.help \ ${HELP}/None.help \ + ${HELP}/NormalizedTriangularSetCategory.help \ ${HELP}/NottinghamGroup.help \ + ${HELP}/NumericalIntegrationCategory.help \ + ${HELP}/NumericalOptimizationCategory.help \ ${HELP}/Octonion.help \ + ${HELP}/OctonionCategory.help \ ${HELP}/OneDimensionalArray.help \ + ${HELP}/OneDimensionalArrayAggregate.help \ + ${HELP}/OpenMath.help \ ${HELP}/Operator.help \ + ${HELP}/OrderedAbelianGroup.help \ + ${HELP}/OrderedAbelianMonoid.help \ + ${HELP}/OrderedAbelianMonoidSup.help \ + ${HELP}/OrderedAbelianSemiGroup.help \ + ${HELP}/OrderedCancellationAbelianMonoid.help \ + ${HELP}/OrderedFinite.help \ ${HELP}/OrderedFreeMonoid.help \ + ${HELP}/OrderedIntegralDomain.help \ + ${HELP}/OrderedMonoid.help \ + ${HELP}/OrderedMultisetAggregate.help \ + ${HELP}/OrderedRing.help \ + ${HELP}/OrderedSet.help \ ${HELP}/OrderedVariableList.help \ ${HELP}/OrderlyDifferentialPolynomial.help \ + ${HELP}/OrdinaryDifferentialEquationsSolverCategory.help \ ${HELP}/PackageForAlgebraicFunctionField.help \ ${HELP}/PackageForAlgebraicFunctionFieldOverFiniteField.help \ ${HELP}/PackageForPoly.help \ + ${HELP}/PAdicIntegerCategory.help \ ${HELP}/ParametrizationPackage.help \ + ${HELP}/PartialDifferentialEquationsSolverCategory.help \ + ${HELP}/PartialDifferentialRing.help \ ${HELP}/PartialFraction.help \ ${HELP}/PartialFractionPackage.help \ + ${HELP}/PartialTranscendentalFunctions.help \ + ${HELP}/Patternable.help \ + ${HELP}/PatternMatchable.help \ ${HELP}/Permanent.help \ ${HELP}/Permutation.help \ + ${HELP}/PermutationCategory.help \ ${HELP}/Places.help \ ${HELP}/PlacesCategory.help \ ${HELP}/PlacesOverPseudoAlgebraicClosureOfFiniteField.help \ ${HELP}/PlaneAlgebraicCurvePlot.help \ ${HELP}/Plcs.help \ ${HELP}/Plot.help \ + ${HELP}/PlottablePlaneCurveCategory.help \ + ${HELP}/PlottableSpaceCurveCategory.help \ + ${HELP}/PointCategory.help \ ${HELP}/Polynomial.help \ + ${HELP}/PolynomialCategory.help \ + ${HELP}/PolynomialFactorizationExplicit.help \ ${HELP}/PolynomialPackageForCurve.help \ + ${HELP}/PolynomialSetCategory.help \ + ${HELP}/PowerSeriesCategory.help \ + ${HELP}/PrimitiveFunctionCategory.help \ + ${HELP}/PrincipalIdealDomain.help \ + ${HELP}/PriorityQueueAggregate.help \ ${HELP}/Product.help \ ${HELP}/ProjectiveAlgebraicSetPackage.help \ ${HELP}/ProjectivePlane.help \ @@ -18204,46 +18352,98 @@ SPADHELP=\ ${HELP}/PseudoAlgebraicClosureOfRationalNumber.help \ ${HELP}/PseudoAlgebraicClosureOfRationalNumberCategory.help \ ${HELP}/Quaternion.help \ + ${HELP}/QuaternionCategory.help \ ${HELP}/QuaternionCategoryFunctions2.help \ ${HELP}/Queue.help \ + ${HELP}/QueueAggregate.help \ + ${HELP}/QuotientFieldCategory.help \ + ${HELP}/RadicalCategory.help \ ${HELP}/RadicalSolvePackage.help \ ${HELP}/RadixExpansion.help \ ${HELP}/RationalFunctionSum.help \ + ${HELP}/RealClosedField.help \ ${HELP}/RealClosure.help \ + ${HELP}/RealConstant.help \ + ${HELP}/RealNumberSystem.help \ + ${HELP}/RealRootCharacterizationCategory.help \ ${HELP}/RealSolvePackage.help \ + ${HELP}/RectangularMatrixCategory.help \ + ${HELP}/RecursiveAggregate.help \ + ${HELP}/RecursivePolynomialCategory.help \ ${HELP}/RegularTriangularSet.help \ + ${HELP}/RegularTriangularSetCategory.help \ + ${HELP}/RetractableTo.help \ + ${HELP}/RightModule.help \ + ${HELP}/Ring.help \ + ${HELP}/Rng.help \ ${HELP}/RomanNumeral.help \ ${HELP}/RootsFindingPackage.help \ ${HELP}/Segment.help \ ${HELP}/SegmentBinding.help \ + ${HELP}/SegmentCategory.help \ + ${HELP}/SegmentExpansionCategory.help \ + ${HELP}/SemiGroup.help \ ${HELP}/Set.help \ + ${HELP}/SetAggregate.help \ + ${HELP}/SetCategory.help \ ${HELP}/SetCategoryWithDegree.help \ + ${HELP}/SExpressionCategory.help \ ${HELP}/SingleInteger.help \ ${HELP}/SparseTable.help \ ${HELP}/SparseMultivariateTaylorSeries.help \ + ${HELP}/SpecialFunctionCategory.help \ ${HELP}/SquareMatrix.help \ + ${HELP}/SquareFreeNormalizedTriangularSetCategory.help \ ${HELP}/SquareFreeRegularTriangularSet.help \ + ${HELP}/SquareFreeRegularTriangularSetCategory.help \ + ${HELP}/SquareMatrixCategory.help \ ${HELP}/Stack.help \ + ${HELP}/StackAggregate.help \ + ${HELP}/StepThrough.help \ ${HELP}/Stream.help \ + ${HELP}/StreamAggregate.help \ ${HELP}/String.help \ + ${HELP}/StringAggregate.help \ + ${HELP}/StringCategory.help \ ${HELP}/StringTable.help \ ${HELP}/Symbol.help \ - ${HELP}/TexFormat.help \ ${HELP}/Table.help \ + ${HELP}/TableAggregate.help \ + ${HELP}/TexFormat.help \ ${HELP}/TextFile.help \ + ${HELP}/ThreeSpaceCategory.help \ + ${HELP}/TranscendentalFunctionCategory.help \ ${HELP}/TransSolvePackage.help \ + ${HELP}/TriangularSetCategory.help \ + ${HELP}/TrigonometricFunctionCategory.help \ ${HELP}/TwoDimensionalArray.help \ + ${HELP}/TwoDimensionalArrayCategory.help \ ${HELP}/TwoDimensionalViewport.help \ + ${HELP}/UnaryRecursiveAggregate.help \ + ${HELP}/UniqueFactorizationDomain.help \ + ${HELP}/UnivariateLaurentSeriesCategory.help \ + ${HELP}/UnivariateLaurentSeriesConstructorCategory.help \ + ${HELP}/UnivariatePolynomialCategory.help \ + ${HELP}/UnivariatePowerSeriesCategory.help \ + ${HELP}/UnivariatePuiseuxSeriesCategory.help \ + ${HELP}/UnivariatePuiseuxSeriesConstructorCategory.help \ ${HELP}/UnivariateSkewPolynomial.help \ + ${HELP}/UnivariateSkewPolynomialCategory.help \ ${HELP}/UnivariatePolynomial.help \ ${HELP}/UnivariateTaylorSeriesCZero.help \ + ${HELP}/UnivariateTaylorSeriesCategory.help \ ${HELP}/UniversalSegment.help \ ${HELP}/Vector.help \ + ${HELP}/VectorCategory.help \ + ${HELP}/VectorSpace.help \ ${HELP}/Void.help \ ${HELP}/WuWenTsunTriangularSet.help \ + ${HELP}/XAlgebra.help \ + ${HELP}/XFreeAlgebra.help \ ${HELP}/XPBWPolynomial.help \ ${HELP}/XPolynomial.help \ ${HELP}/XPolynomialRing.help \ + ${HELP}/XPolynomialsCat.help \ ${HELP}/ZeroDimensionalSolvePackage.help \ ${HELP}/dcabs1.help \ ${HELP}/dasum.help \ @@ -18259,99 +18459,200 @@ is put into a int/Makefile.algebra and then executed by make. TESTSYS= ${OBJ}/${SYS}/bin/interpsys REGRESS= \ + AbelianGroup.regress \ + AbelianMonoid.regress \ + AbelianMonoidRing.regress \ + AbelianSemiGroup.regress \ AffineAlgebraicSetComputeWithGroebnerBasis.regress \ AffineAlgebraicSetComputeWithResultant.regress \ AffinePlane.regress \ AffinePlaneOverPseudoAlgebraicClosureOfFiniteField.regress \ AffineSpace.regress \ AffineSpaceCategory.regress \ + Aggregate.regress \ + Algebra.regress \ AlgebraicallyClosedField.regress \ + AlgebraicallyClosedFunctionSpace.regress \ Any.regress \ ApplicationProgramInterface.regress \ + ArcHyperbolicFunctionCategory.regress \ + ArcTrigonometricFunctionCategory.regress \ ArrayStack.regress \ AssociationList.regress \ + AssociationListAggregate.regress \ BalancedBinaryTree.regress \ + BagAggregate.regress \ BasicOperator.regress \ + BasicType.regress \ Bezier.regress \ + BiModule.regress \ BinaryExpansion.regress \ + BinaryRecursiveAggregate.regress \ BinarySearchTree.regress \ + BinaryTreeCategory.regress \ + BitAggregate.regress \ BlasLevelOne.regress \ BlowUpMethodCategory.regress \ BlowUpPackage.regress \ BlowUpWithHamburgerNoether.regress \ BlowUpWithQuadTrans.regress \ + CachableSet.regress \ + CancellationAbelianMonoid.regress \ CardinalNumber.regress \ CartesianTensor.regress \ Character.regress \ CharacterClass.regress \ + CharacteristicNonZero.regress \ + CharacteristicZero.regress \ CliffordAlgebra.regress \ + CoercibleTo.regress \ + Collection.regress \ CombinatorialFunction.regress \ + CombinatorialFunctionCategory.regress \ + CombinatorialOpsCategory.regress \ + CommutativeRing.regress \ Complex.regress \ + ComplexCategory.regress \ ContinuedFraction.regress \ + ConvertibleTo.regress \ CycleIndicators.regress \ + Dequeue.regress \ + DequeueAggregate.regress \ DeRhamComplex.regress \ DecimalExpansion.regress \ - Dequeue.regress \ DesingTree.regress \ DesingTreeCategory.regress \ DesingTreePackage.regress \ + Dictionary.regress \ + DictionaryOperations.regress \ + DifferentialExtension.regress \ + DifferentialPolynomialCategory.regress \ + DifferentialRing.regress \ + DifferentialVariableCategory.regress \ + DirectProductCategory.regress \ DistributedMultivariatePolynomial.regress \ + DivisionRing.regress \ Divisor.regress \ DivisorCategory.regress \ DoubleFloat.regress \ + DoublyLinkedAggregate.regress \ ElementaryFunction.regress \ + ElementaryFunctionCategory.regress \ + Eltable.regress \ + EltableAggregate.regress \ + EntireRing.regress \ EqTable.regress \ Equation.regress \ - Expression.regress \ + EuclideanDomain.regress \ EuclideanGroebnerBasisPackage.regress \ + Evalable.regress \ + Expression.regress \ + ExpressionSpace.regress \ + ExtensibleLinearAggregate.regress \ + ExtensionField.regress \ Factored.regress \ FactoredFunctions2.regress \ FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber.regress \ FactorisationOverPseudoAlgebraicClosureOfRationalNumber.regress \ + Field.regress \ + FieldOfPrimeCharacteristic.regress \ File.regress \ + FileCategory.regress \ FileName.regress \ + FileNameCategory.regress \ + Finite.regress \ + FiniteAbelianMonoidRing.regress \ + FiniteAlgebraicExtensionField.regress \ + FiniteDivisorCategory.regress \ + FiniteFieldCategory.regress \ FiniteFieldFactorizationWithSizeParseBySideEffect.regress \ FiniteFieldSquareFreeDecomposition.regress \ + FiniteLinearAggregate.regress \ + FiniteRankAlgebra.regress \ + FiniteRankNonAssociativeAlgebra.regress \ + FiniteSetAggregate.regress \ FlexibleArray.regress \ Float.regress \ + FloatingPointSystem.regress \ + FortranFunctionCategory.regress \ + FortranMachineTypeCategory.regress \ + FortranMatrixCategory.regress \ + FortranMatrixFunctionCategory.regress \ + FortranProgramCategory.regress \ + FortranVectorCategory.regress \ + FortranVectorFunctionCategory.regress \ Fraction.regress \ + FramedAlgebra.regress \ + FramedNonAssociativeAlgebra.regress \ + FreeAbelianMonoidCategory.regress \ + FreeLieAlgebra.regress \ + FreeModuleCat.regress \ FullPartialFractionExpansion.regress \ + FullyEvalableOver.regress \ + FullyLinearlyExplicitRingOver.regress \ + FullyPatternMatchable.regress \ + FullyRetractableTo.regress \ + FunctionFieldCategory.regress \ + FunctionSpace.regress \ + GcdDomain.regress \ GeneralDistributedMultivariatePolynomial.regress \ GeneralPackageForAlgebraicFunctionField.regress \ GeneralSparseTable.regress \ + GradedAlgebra.regress \ + GradedModule.regress \ GroebnerFactorizationPackage.regress \ GroebnerPackage.regress \ + Group.regress \ Heap.regress \ HexadecimalExpansion.regress \ + HomogeneousAggregate.regress \ HomogeneousDistributedMultivariatePolynomial.regress \ + HyperbolicFunctionCategory.regress \ + IndexedAggregate.regress \ IndexedBits.regress \ + IndexedDirectProductCategory.regress \ InfClsPt.regress \ InfinitlyClosePoint.regress \ InfinitlyClosePointCategory.regress \ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField.regress \ + InnerEvalable.regress \ Integer.regress \ IntegerCombinatoricFunctions.regress \ IntegerLinearDependence.regress \ + IntegerNumberSystem.regress \ IntegerNumberTheoryFunctions.regress \ + IntegralDomain.regress \ InterfaceGroebnerPackage.regress \ InterpolateFormsPackage.regress \ IntersectionDivisorPackage.regress \ Interval.regress \ + IntervalCategory.regress \ Kernel.regress \ KeyedAccessFile.regress \ + KeyedDictionary.regress \ + LazyStreamAggregate.regress \ LazardSetSolvingPackage.regress \ + LeftAlgebra.regress \ + LeftModule.regress \ LexTriangularPackage.regress \ Library.regress \ + LieAlgebra.regress \ LieExponentials.regress \ LiePolynomial.regress \ + LinearlyExplicitRingOver.regress \ + LinearAggregate.regress \ LinearOrdinaryDifferentialOperator.regress \ LinearOrdinaryDifferentialOperator1.regress \ LinearOrdinaryDifferentialOperator2.regress \ + LinearOrdinaryDifferentialOperatorCategory.regress \ LinearSystemFromPowerSeriesPackage.regress \ + ListAggregate.regress \ + LiouvillianFunctionCategory.regress \ List.regress \ LinesOpPack.regress \ LocalParametrizationOfSimplePointPackage.regress \ LocalPowerSeriesCategory.regress \ + Logic.regress \ LyndonWord.regress \ Magma.regress \ MathMLFormat.regress \ @@ -18361,34 +18662,81 @@ REGRESS= \ MappingPackage3.regress \ Matrix.regress \ MatrixCategory.regress \ + Module.regress \ + Monad.regress \ + MonadWithUnit.regress \ + MonogenicAlgebra.regress \ + MonogenicLinearOperator.regress \ + Monoid.regress \ + MultiDictionary.regress \ Multiset.regress \ + MultisetAggregate.regress \ MultivariatePolynomial.regress \ + MultivariateTaylorSeriesCategory.regress \ NeitherSparseOrDensePowerSeries.regress \ NewtonPolygon.regress \ + NonAssociativeAlgebra.regress \ + NonAssociativeRing.regress \ + NonAssociativeRng.regress \ None.regress \ + NormalizedTriangularSetCategory.regress \ NottinghamGroup.regress \ + NumericalIntegrationCategory.regress \ + NumericalOptimizationCategory.regress \ Octonion.regress \ + OctonionCategory.regress \ OneDimensionalArray.regress \ + OneDimensionalArrayAggregate.regress \ + OpenMath.regress \ Operator.regress \ + OrderedAbelianGroup.regress \ + OrderedAbelianMonoid.regress \ + OrderedAbelianMonoidSup.regress \ + OrderedAbelianSemiGroup.regress \ + OrderedCancellationAbelianMonoid.regress \ + OrderedFinite.regress \ OrderedFreeMonoid.regress \ + OrderedIntegralDomain.regress \ + OrderedMonoid.regress \ + OrderedMultisetAggregate.regress \ + OrderedRing.regress \ + OrderedSet.regress \ OrderedVariableList.regress \ OrderlyDifferentialPolynomial.regress \ + OrdinaryDifferentialEquationsSolverCategory.regress \ PackageForAlgebraicFunctionField.regress \ PackageForAlgebraicFunctionFieldOverFiniteField.regress \ PackageForPoly.regress \ + PAdicIntegerCategory.regress \ ParametrizationPackage.regress \ + PartialDifferentialEquationsSolverCategory.regress \ + PartialDifferentialRing.regress \ PartialFraction.regress \ PartialFractionPackage.regress \ + PartialTranscendentalFunctions.regress \ + Patternable.regress \ + PatternMatchable.regress \ Permanent.regress \ Permutation.regress \ + PermutationCategory.regress \ Places.regress \ PlacesCategory.regress \ PlacesOverPseudoAlgebraicClosureOfFiniteField.regress \ PlaneAlgebraicCurvePlot.regress \ Plcs.regress \ Plot.regress \ + PlottablePlaneCurveCategory.regress \ + PlottableSpaceCurveCategory.regress \ + PointCategory.regress \ Polynomial.regress \ + PolynomialCategory.regress \ + PolynomialFactorizationExplicit.regress \ PolynomialPackageForCurve.regress \ + PolynomialSetCategory.regress \ + PowerSeriesCategory.regress \ + PrimitiveFunctionCategory.regress \ + PrincipalIdealDomain.regress \ + PriorityQueueAggregate.regress \ Product.regress \ ProjectiveAlgebraicSetPackage.regress \ ProjectivePlane.regress \ @@ -18403,44 +18751,96 @@ REGRESS= \ PseudoAlgebraicClosureOfRationalNumber.regress \ PseudoAlgebraicClosureOfRationalNumberCategory.regress \ Quaternion.regress \ + QuaternionCategory.regress \ QuaternionCategoryFunctions2.regress \ Queue.regress \ + QueueAggregate.regress \ + QuotientFieldCategory.regress \ + RadicalCategory.regress \ RadicalSolvePackage.regress \ RadixExpansion.regress \ RationalFunctionSum.regress \ + RealClosedField.regress \ RealClosure.regress \ + RealConstant.regress \ + RealNumberSystem.regress \ + RealRootCharacterizationCategory.regress \ RealSolvePackage.regress \ + RectangularMatrixCategory.regress \ + RecursiveAggregate.regress \ + RecursivePolynomialCategory.regress \ RegularTriangularSet.regress \ + RegularTriangularSetCategory.regress \ + RetractableTo.regress \ + RightModule.regress \ + Ring.regress \ + Rng.regress \ RomanNumeral.regress \ RootsFindingPackage.regress \ Segment.regress \ + SegmentCategory.regress \ + SegmentExpansionCategory.regress \ + SemiGroup.regress \ Set.regress \ + SetAggregate.regress \ + SetCategory.regress \ SetCategoryWithDegree.regress \ + SExpressionCategory.regress \ SingleInteger.regress \ SparseTable.regress \ SparseMultivariateTaylorSeries.regress \ + SpecialFunctionCategory.regress \ SquareMatrix.regress \ + SquareFreeNormalizedTriangularSetCategory.regress \ SquareFreeRegularTriangularSet.regress \ + SquareFreeRegularTriangularSetCategory.regress \ + SquareMatrixCategory.regress \ Stack.regress \ + StackAggregate.regress \ + StepThrough.regress \ Stream.regress \ + StreamAggregate.regress \ String.regress \ + StringAggregate.regress \ + StringCategory.regress \ StringTable.regress \ Symbol.regress \ Table.regress \ + TableAggregate.regress \ TexFormat.regress \ TextFile.regress \ + ThreeSpaceCategory.regress \ + TranscendentalFunctionCategory.regress \ TransSolvePackage.regress \ + TriangularSetCategory.regress \ + TrigonometricFunctionCategory.regress \ TwoDimensionalArray.regress \ + TwoDimensionalArrayCategory.regress \ + UnaryRecursiveAggregate.regress \ + UniqueFactorizationDomain.regress \ + UnivariateLaurentSeriesCategory.regress \ + UnivariateLaurentSeriesConstructorCategory.regress \ + UnivariatePolynomialCategory.regress \ + UnivariatePowerSeriesCategory.regress \ + UnivariatePuiseuxSeriesCategory.regress \ + UnivariatePuiseuxSeriesConstructorCategory.regress \ UnivariateSkewPolynomial.regress \ + UnivariateSkewPolynomialCategory.regress \ UnivariatePolynomial.regress \ UnivariateTaylorSeriesCZero.regress \ + UnivariateTaylorSeriesCategory.regress \ UniversalSegment.regress \ Vector.regress \ + VectorCategory.regress \ + VectorSpace.regress \ Void.regress \ WuWenTsunTriangularSet.regress \ + XAlgebra.regress \ + XFreeAlgebra.regress \ XPBWPolynomial.regress \ XPolynomial.regress \ XPolynomialRing.regress \ + XPolynomialsCat.regress \ ZeroDimensionalSolvePackage.regress \ dcabs1.regress \ dasum.regress \ @@ -18471,6 +18871,54 @@ all: ${REGRESS} @echo algebra test cases complete. @ <>= +${HELP}/AbelianGroup.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create AbelianGroup.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"AbelianGroup.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/AbelianGroup.help + @cp ${HELP}/AbelianGroup.help ${HELP}/ABELGRP.help + @${TANGLE} -R"AbelianGroup.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/AbelianGroup.input + @echo "AbelianGroup (ABELGRP)" >>${HELPFILE} + +${HELP}/AbelianMonoid.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create AbelianMonoid.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"AbelianMonoid.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/AbelianMonoid.help + @cp ${HELP}/AbelianMonoid.help ${HELP}/ABELMON.help + @${TANGLE} -R"AbelianMonoid.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/AbelianMonoid.input + @echo "AbelianMonoid (ABELMON)" >>${HELPFILE} + +${HELP}/AbelianMonoidRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create AbelianMonoidRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"AbelianMonoidRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/AbelianMonoidRing.help + @cp ${HELP}/AbelianMonoidRing.help ${HELP}/AMR.help + @${TANGLE} -R"AbelianMonoidRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/AbelianMonoidRing.input + @echo "AbelianMonoidRing (AMR)" >>${HELPFILE} + +${HELP}/AbelianSemiGroup.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create AbelianSemiGroup.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"AbelianSemiGroup.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/AbelianSemiGroup.help + @cp ${HELP}/AbelianSemiGroup.help ${HELP}/ABELSG.help + @${TANGLE} -R"AbelianSemiGroup.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/AbelianSemiGroup.input + @echo "AbelianSemiGroup (ABELSG)" >>${HELPFILE} + ${HELP}/AffineAlgebraicSetComputeWithGroebnerBasis.help: \ ${BOOKS}/bookvol10.4.pamphlet @echo 7000 create \ @@ -18561,6 +19009,30 @@ ${HELP}/AffineSpaceCategory.help: ${BOOKS}/bookvol10.2.pamphlet >${INPUT}/AffineSpaceCategory.input @echo "AffineSpaceCategory (AFSPCAT)" >>${HELPFILE} +${HELP}/Aggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Aggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Aggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Aggregate.help + @cp ${HELP}/Aggregate.help ${HELP}/AGG.help + @${TANGLE} -R"Aggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Aggregate.input + @echo "Aggregate (AGG)" >>${HELPFILE} + +${HELP}/Algebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Algebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Algebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Algebra.help + @cp ${HELP}/Algebra.help ${HELP}/ALGEBRA.help + @${TANGLE} -R"Algebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Algebra.input + @echo "Algebra (ALGEBRA)" >>${HELPFILE} + ${HELP}/AlgebraicallyClosedField.help: ${BOOKS}/bookvol10.2.pamphlet @echo 7006 create AlgebraicallyClosedField.help from \ ${BOOKS}/bookvol10.2.pamphlet @@ -18573,6 +19045,18 @@ ${HELP}/AlgebraicallyClosedField.help: ${BOOKS}/bookvol10.2.pamphlet >${INPUT}/AlgebraicallyClosedField.input @echo "AlgebraicallyClosedField (ACF)" >>${HELPFILE} +${HELP}/AlgebraicallyClosedFunctionSpace.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create AlgebraicallyClosedFunctionSpace.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"AlgebraicallyClosedFunctionSpace.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/AlgebraicallyClosedFunctionSpace.help + @cp ${HELP}/AlgebraicallyClosedFunctionSpace.help ${HELP}/ACFS.help + @${TANGLE} -R"AlgebraicallyClosedFunctionSpace.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/AlgebraicallyClosedFunctionSpace.input + @echo "AlgebraicallyClosedFunctionSpace (ACFS)" >>${HELPFILE} + ${HELP}/Any.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7007 create Any.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Any.help" ${BOOKS}/bookvol10.3.pamphlet >${HELP}/Any.help @@ -18593,6 +19077,30 @@ ${HELP}/ApplicationProgramInterface.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/ApplicationProgramInterface.input @echo "ApplicationProgramInterface (API)" >>${HELPFILE} +${HELP}/ArcHyperbolicFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ArcHyperbolicFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ArcHyperbolicFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ArcHyperbolicFunctionCategory.help + @cp ${HELP}/ArcHyperbolicFunctionCategory.help ${HELP}/AHYP.help + @${TANGLE} -R"ArcHyperbolicFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ArcHyperbolicFunctionCategory.input + @echo "ArcHyperbolicFunctionCategory (AHYP)" >>${HELPFILE} + +${HELP}/ArcTrigonometricFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ArcTrigonometricFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ArcTrigonometricFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ArcTrigonometricFunctionCategory.help + @cp ${HELP}/ArcTrigonometricFunctionCategory.help ${HELP}/ATRIG.help + @${TANGLE} -R"ArcTrigonometricFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ArcTrigonometricFunctionCategory.input + @echo "ArcTrigonometricFunctionCategory (ATRIG)" >>${HELPFILE} + ${HELP}/ArrayStack.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7010 create ArrayStack.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"ArrayStack.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -18612,6 +19120,18 @@ ${HELP}/AssociationList.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/AssociationList.input @echo "AssociationList (ALIST)" >>${HELPFILE} +${HELP}/AssociationListAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create AssociationListAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"AssociationListAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/AssociationListAggregate.help + @cp ${HELP}/AssociationListAggregate.help ${HELP}/ALAGG.help + @${TANGLE} -R"AssociationListAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/AssociationListAggregate.input + @echo "AssociationListAggregate (ALAGG)" >>${HELPFILE} + ${HELP}/BalancedBinaryTree.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7030 create BalancedBinaryTree.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18622,6 +19142,18 @@ ${HELP}/BalancedBinaryTree.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/BalancedBinaryTree.input @echo "BalancedBinaryTree (BBTREE)" >>${HELPFILE} +${HELP}/BagAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create BagAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"BagAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/BagAggregate.help + @cp ${HELP}/BagAggregate.help ${HELP}/BGAGG.help + @${TANGLE} -R"BagAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/BagAggregate.input + @echo "BagAggregate (BGAGG)" >>${HELPFILE} + ${HELP}/BasicOperator.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7040 create BasicOperator.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"BasicOperator.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -18631,6 +19163,18 @@ ${HELP}/BasicOperator.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/BasicOperator.input @echo "BasicOperator (BOP)" >>${HELPFILE} +${HELP}/BasicType.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create BasicType.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"BasicType.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/BasicType.help + @cp ${HELP}/BasicType.help ${HELP}/BASTYPE.help + @${TANGLE} -R"BasicType.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/BasicType.input + @echo "BasicType (BASTYPE)" >>${HELPFILE} + ${HELP}/Bezier.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7050 create Bezier.help from ${BOOKS}/bookvol10.4.pamphlet @${TANGLE} -R"Bezier.help" ${BOOKS}/bookvol10.4.pamphlet \ @@ -18640,6 +19184,18 @@ ${HELP}/Bezier.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/Bezier.input @echo "Bezier (BEZIER)" >>${HELPFILE} +${HELP}/BiModule.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create BiModule.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"BiModule.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/BiModule.help + @cp ${HELP}/BiModule.help ${HELP}/BMODULE.help + @${TANGLE} -R"BiModule.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/BiModule.input + @echo "BiModule (BMODULE)" >>${HELPFILE} + ${HELP}/BinaryExpansion.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7060 create BinaryExpansion.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18650,6 +19206,18 @@ ${HELP}/BinaryExpansion.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/BinaryExpansion.input @echo "BinaryExpansion (BINARY)" >>${HELPFILE} +${HELP}/BinaryRecursiveAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create BinaryRecursiveAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"BinaryRecursiveAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/BinaryRecursiveAggregate.help + @cp ${HELP}/BinaryRecursiveAggregate.help ${HELP}/BRAGG.help + @${TANGLE} -R"BinaryRecursiveAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/BinaryRecursiveAggregate.input + @echo "BinaryRecursiveAggregate (BRAGG)" >>${HELPFILE} + ${HELP}/BinarySearchTree.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7070 create BinarySearchTree.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18660,6 +19228,30 @@ ${HELP}/BinarySearchTree.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/BinarySearchTree.input @echo "BinarySearchTree (BSTREE)" >>${HELPFILE} +${HELP}/BinaryTreeCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create BinaryTreeCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"BinaryTreeCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/BinaryTreeCategory.help + @cp ${HELP}/BinaryTreeCategory.help ${HELP}/BTCAT.help + @${TANGLE} -R"BinaryTreeCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/BinaryTreeCategory.input + @echo "BinaryTreeCategory (BTCAT)" >>${HELPFILE} + +${HELP}/BitAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create BitAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"BitAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/BitAggregate.help + @cp ${HELP}/BitAggregate.help ${HELP}/BTAGG.help + @${TANGLE} -R"BitAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/BitAggregate.input + @echo "BitAggregate (BTAGG)" >>${HELPFILE} + ${HELP}/BlasLevelOne.help: ${BOOKS}/bookvol10.5.pamphlet @echo 7080 create BlasLevelOne.help from \ ${BOOKS}/bookvol10.5.pamphlet @@ -18718,6 +19310,30 @@ ${HELP}/BlowUpWithQuadTrans.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/BlowUpWithQuadTrans.input @echo "BlowUpWithQuadTrans (BLQT)" >>${HELPFILE} +${HELP}/CachableSet.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CachableSet.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CachableSet.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CachableSet.help + @cp ${HELP}/CachableSet.help ${HELP}/CACHSET.help + @${TANGLE} -R"CachableSet.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CachableSet.input + @echo "CachableSet (CACHSET)" >>${HELPFILE} + +${HELP}/CancellationAbelianMonoid.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CancellationAbelianMonoid.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CancellationAbelianMonoid.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CancellationAbelianMonoid.help + @cp ${HELP}/CancellationAbelianMonoid.help ${HELP}/CABMON.help + @${TANGLE} -R"CancellationAbelianMonoid.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CancellationAbelianMonoid.input + @echo "CancellationAbelianMonoid (CABMON)" >>${HELPFILE} + ${HELP}/CardinalNumber.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7086 create CardinalNumber.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18757,6 +19373,30 @@ ${HELP}/CharacterClass.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/CharacterClass.input @echo "CharacterClass (CCLASS)" >>${HELPFILE} +${HELP}/CharacteristicNonZero.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CharacteristicNonZero.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CharacteristicNonZero.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CharacteristicNonZero.help + @cp ${HELP}/CharacteristicNonZero.help ${HELP}/CHARNZ.help + @${TANGLE} -R"CharacteristicNonZero.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CharacteristicNonZero.input + @echo "CharacteristicNonZero (CHARNZ)" >>${HELPFILE} + +${HELP}/CharacteristicZero.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CharacteristicZero.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CharacteristicZero.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CharacteristicZero.help + @cp ${HELP}/CharacteristicZero.help ${HELP}/CHARZ.help + @${TANGLE} -R"CharacteristicZero.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CharacteristicZero.input + @echo "CharacteristicZero (CHARZ)" >>${HELPFILE} + ${HELP}/CliffordAlgebra.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7120 create CliffordAlgebra.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18767,6 +19407,30 @@ ${HELP}/CliffordAlgebra.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/CliffordAlgebra.input @echo "CliffordAlgebra (CLIF)" >>${HELPFILE} +${HELP}/CoercibleTo.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CoercibleTo.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CoercibleTo.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CoercibleTo.help + @cp ${HELP}/CoercibleTo.help ${HELP}/KOERCE.help + @${TANGLE} -R"CoercibleTo.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CoercibleTo.input + @echo "CoercibleTo (KOERCE)" >>${HELPFILE} + +${HELP}/Collection.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Collection.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Collection.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Collection.help + @cp ${HELP}/Collection.help ${HELP}/CLAGG.help + @${TANGLE} -R"Collection.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Collection.input + @echo "Collection (CLAGG)" >>${HELPFILE} + ${HELP}/CombinatorialFunction.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7130 create CombinatorialFunction.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -18779,6 +19443,42 @@ ${HELP}/CombinatorialFunction.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/CombinatorialFunction.input @echo "CombinatorialFunction (COMBF)" >>${HELPFILE} +${HELP}/CombinatorialFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CombinatorialFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CombinatorialFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CombinatorialFunctionCategory.help + @cp ${HELP}/CombinatorialFunctionCategory.help ${HELP}/CFCAT.help + @${TANGLE} -R"CombinatorialFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CombinatorialFunctionCategory.input + @echo "CombinatorialFunctionCategory (CFCAT)" >>${HELPFILE} + +${HELP}/CombinatorialOpsCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CombinatorialOpsCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CombinatorialOpsCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CombinatorialOpsCategory.help + @cp ${HELP}/CombinatorialOpsCategory.help ${HELP}/COMBOPC.help + @${TANGLE} -R"CombinatorialOpsCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CombinatorialOpsCategory.input + @echo "CombinatorialOpsCategory (COMBOPC)" >>${HELPFILE} + +${HELP}/CommutativeRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create CommutativeRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"CommutativeRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/CommutativeRing.help + @cp ${HELP}/CommutativeRing.help ${HELP}/COMRING.help + @${TANGLE} -R"CommutativeRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/CommutativeRing.input + @echo "CommutativeRing (COMRING)" >>${HELPFILE} + ${HELP}/Complex.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7140 create Complex.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Complex.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -18788,6 +19488,18 @@ ${HELP}/Complex.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Complex.input @echo "Complex (COMPLEX)" >>${HELPFILE} +${HELP}/ComplexCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ComplexCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ComplexCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ComplexCategory.help + @cp ${HELP}/ComplexCategory.help ${HELP}/COMPCAT.help + @${TANGLE} -R"ComplexCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ComplexCategory.input + @echo "ComplexCategory (COMPCAT)" >>${HELPFILE} + ${HELP}/ContinuedFraction.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7150 create ContinuedFraction.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18798,6 +19510,18 @@ ${HELP}/ContinuedFraction.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/ContinuedFraction.input @echo "ContinuedFraction (CONTFRAC)" >>${HELPFILE} +${HELP}/ConvertibleTo.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ConvertibleTo.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ConvertibleTo.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ConvertibleTo.help + @cp ${HELP}/ConvertibleTo.help ${HELP}/KONVERT.help + @${TANGLE} -R"ConvertibleTo.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ConvertibleTo.input + @echo "ConvertibleTo (KONVERT)" >>${HELPFILE} + ${HELP}/CycleIndicators.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7160 create CycleIndicators.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -18808,6 +19532,27 @@ ${HELP}/CycleIndicators.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/CycleIndicators.input @echo "CycleIndicators (CYCLES)" >>${HELPFILE} +${HELP}/Dequeue.help: ${BOOKS}/bookvol10.3.pamphlet + @echo 7190 create Dequeue.help from ${BOOKS}/bookvol10.3.pamphlet + @${TANGLE} -R"Dequeue.help" ${BOOKS}/bookvol10.3.pamphlet \ + >${HELP}/Dequeue.help + @cp ${HELP}/Dequeue.help ${HELP}/DEQUEUE.help + @${TANGLE} -R"Dequeue.input" ${BOOKS}/bookvol10.3.pamphlet \ + >${INPUT}/Dequeue.input + @echo "Dequeue (DEQUEUE)" >>${HELPFILE} + +${HELP}/DequeueAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DequeueAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DequeueAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DequeueAggregate.help + @cp ${HELP}/DequeueAggregate.help ${HELP}/DQAGG.help + @${TANGLE} -R"DequeueAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DequeueAggregate.input + @echo "DequeueAggregate (DQAGG)" >>${HELPFILE} + ${HELP}/DeRhamComplex.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7170 create DeRhamComplex.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"DeRhamComplex.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -18827,15 +19572,6 @@ ${HELP}/DecimalExpansion.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/DecimalExpansion.input @echo "DecimalExpansion (DECIMAL)" >>${HELPFILE} -${HELP}/Dequeue.help: ${BOOKS}/bookvol10.3.pamphlet - @echo 7190 create Dequeue.help from ${BOOKS}/bookvol10.3.pamphlet - @${TANGLE} -R"Dequeue.help" ${BOOKS}/bookvol10.3.pamphlet \ - >${HELP}/Dequeue.help - @cp ${HELP}/Dequeue.help ${HELP}/DEQUEUE.help - @${TANGLE} -R"Dequeue.input" ${BOOKS}/bookvol10.3.pamphlet \ - >${INPUT}/Dequeue.input - @echo "Dequeue (DEQUEUE)" >>${HELPFILE} - ${HELP}/DesingTree.help: \ ${BOOKS}/bookvol10.3.pamphlet @echo 7295 create DesingTree.help \ @@ -18875,6 +19611,90 @@ ${HELP}/DesingTreePackage.help: \ >${INPUT}/DesingTreePackage.input @echo "DesingTreePackage (DTP)" >>${HELPFILE} +${HELP}/Dictionary.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Dictionary.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Dictionary.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Dictionary.help + @cp ${HELP}/Dictionary.help ${HELP}/DIAGG.help + @${TANGLE} -R"Dictionary.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Dictionary.input + @echo "Dictionary (DIAGG)" >>${HELPFILE} + +${HELP}/DictionaryOperations.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DictionaryOperations.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DictionaryOperations.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DictionaryOperations.help + @cp ${HELP}/DictionaryOperations.help ${HELP}/DIOPS.help + @${TANGLE} -R"DictionaryOperations.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DictionaryOperations.input + @echo "DictionaryOperations (DIOPS)" >>${HELPFILE} + +${HELP}/DifferentialExtension.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DifferentialExtension.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DifferentialExtension.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DifferentialExtension.help + @cp ${HELP}/DifferentialExtension.help ${HELP}/DIFEXT.help + @${TANGLE} -R"DifferentialExtension.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DifferentialExtension.input + @echo "DifferentialExtension (DIFEXT)" >>${HELPFILE} + +${HELP}/DifferentialPolynomialCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DifferentialPolynomialCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DifferentialPolynomialCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DifferentialPolynomialCategory.help + @cp ${HELP}/DifferentialPolynomialCategory.help ${HELP}/DPOLCAT.help + @${TANGLE} -R"DifferentialPolynomialCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DifferentialPolynomialCategory.input + @echo "DifferentialPolynomialCategory (DPOLCAT)" >>${HELPFILE} + +${HELP}/DifferentialRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DifferentialRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DifferentialRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DifferentialRing.help + @cp ${HELP}/DifferentialRing.help ${HELP}/DIFRING.help + @${TANGLE} -R"DifferentialRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DifferentialRing.input + @echo "DifferentialRing (DIFRING)" >>${HELPFILE} + +${HELP}/DifferentialVariableCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DifferentialVariableCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DifferentialVariableCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DifferentialVariableCategory.help + @cp ${HELP}/DifferentialVariableCategory.help ${HELP}/DVARCAT.help + @${TANGLE} -R"DifferentialVariableCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DifferentialVariableCategory.input + @echo "DifferentialVariableCategory (DVARCAT)" >>${HELPFILE} + +${HELP}/DirectProductCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DirectProductCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DirectProductCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DirectProductCategory.help + @cp ${HELP}/DirectProductCategory.help ${HELP}/DIRPCAT.help + @${TANGLE} -R"DirectProductCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DirectProductCategory.input + @echo "DirectProductCategory (DIRPCAT)" >>${HELPFILE} + ${HELP}/DistributedMultivariatePolynomial.help: \ ${BOOKS}/bookvol10.3.pamphlet @echo 7299 create DistributedMultivariatePolynomial.help \ @@ -18888,6 +19708,18 @@ ${HELP}/DistributedMultivariatePolynomial.help: \ >${INPUT}/DistributedMultivariatePolynomial.input @echo "DistributedMultivariatePolynomial (DMP)" >>${HELPFILE} +${HELP}/DivisionRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DivisionRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DivisionRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DivisionRing.help + @cp ${HELP}/DivisionRing.help ${HELP}/DIVRING.help + @${TANGLE} -R"DivisionRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DivisionRing.input + @echo "DivisionRing (DIVRING)" >>${HELPFILE} + ${HELP}/Divisor.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7205 create Divisor.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -18917,6 +19749,18 @@ ${HELP}/DoubleFloat.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/DoubleFloat.input @echo "DoubleFloat (DFLOAT)" >>${HELPFILE} +${HELP}/DoublyLinkedAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create DoublyLinkedAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"DoublyLinkedAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/DoublyLinkedAggregate.help + @cp ${HELP}/DoublyLinkedAggregate.help ${HELP}/DLAGG.help + @${TANGLE} -R"DoublyLinkedAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/DoublyLinkedAggregate.input + @echo "DoublyLinkedAggregate (DLAGG)" >>${HELPFILE} + ${HELP}/ElementaryFunction.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7220 create ElementaryFunction.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -18927,6 +19771,54 @@ ${HELP}/ElementaryFunction.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/ElementaryFunction.input @echo "ElementaryFunction (EF)" >>${HELPFILE} +${HELP}/ElementaryFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ElementaryFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ElementaryFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ElementaryFunctionCategory.help + @cp ${HELP}/ElementaryFunctionCategory.help ${HELP}/ELEMFUN.help + @${TANGLE} -R"ElementaryFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ElementaryFunctionCategory.input + @echo "ElementaryFunctionCategory (ELEMFUN)" >>${HELPFILE} + +${HELP}/Eltable.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Eltable.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Eltable.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Eltable.help + @cp ${HELP}/Eltable.help ${HELP}/ELTAB.help + @${TANGLE} -R"Eltable.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Eltable.input + @echo "Eltable (ELTAB)" >>${HELPFILE} + +${HELP}/EltableAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create EltableAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"EltableAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/EltableAggregate.help + @cp ${HELP}/EltableAggregate.help ${HELP}/ELTAGG.help + @${TANGLE} -R"EltableAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/EltableAggregate.input + @echo "EltableAggregate (ELTAGG)" >>${HELPFILE} + +${HELP}/EntireRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create EntireRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"EntireRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/EntireRing.help + @cp ${HELP}/EntireRing.help ${HELP}/ENTIRER.help + @${TANGLE} -R"EntireRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/EntireRing.input + @echo "EntireRing (ENTIRER)" >>${HELPFILE} + ${HELP}/EqTable.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7230 create EqTable.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"EqTable.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -18945,6 +19837,30 @@ ${HELP}/Equation.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Equation.input @echo "Equation (EQ)" >>${HELPFILE} +${HELP}/ExpressionSpace.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ExpressionSpace.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ExpressionSpace.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ExpressionSpace.help + @cp ${HELP}/ExpressionSpace.help ${HELP}/ES.help + @${TANGLE} -R"ExpressionSpace.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ExpressionSpace.input + @echo "ExpressionSpace (ES)" >>${HELPFILE} + +${HELP}/ExtensibleLinearAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ExtensibleLinearAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ExtensibleLinearAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ExtensibleLinearAggregate.help + @cp ${HELP}/ExtensibleLinearAggregate.help ${HELP}/ELAGG.help + @${TANGLE} -R"ExtensibleLinearAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ExtensibleLinearAggregate.input + @echo "ExtensibleLinearAggregate (ELAGG)" >>${HELPFILE} + ${HELP}/EuclideanGroebnerBasisPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7250 create EuclideanGroebnerBasisPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -18957,6 +19873,30 @@ ${HELP}/EuclideanGroebnerBasisPackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/EuclideanGroebnerBasisPackage.input @echo "EuclideanGroebnerBasisPackage (GBEUCLID)" >>${HELPFILE} +${HELP}/EuclideanDomain.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create EuclideanDomain.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"EuclideanDomain.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/EuclideanDomain.help + @cp ${HELP}/EuclideanDomain.help ${HELP}/EUCDOM.help + @${TANGLE} -R"EuclideanDomain.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/EuclideanDomain.input + @echo "EuclideanDomain (EUCDOM)" >>${HELPFILE} + +${HELP}/Evalable.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Evalable.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Evalable.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Evalable.help + @cp ${HELP}/Evalable.help ${HELP}/EVALAB.help + @${TANGLE} -R"Evalable.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Evalable.input + @echo "Evalable (EVALAB)" >>${HELPFILE} + ${HELP}/Expression.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7260 create Expression.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Expression.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -18966,6 +19906,18 @@ ${HELP}/Expression.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Expression.input @echo "Expression (EXPR)" >>${HELPFILE} +${HELP}/ExtensionField.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ExtensionField.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ExtensionField.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ExtensionField.help + @cp ${HELP}/ExtensionField.help ${HELP}/XF.help + @${TANGLE} -R"ExtensionField.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ExtensionField.input + @echo "ExtensionField (XF)" >>${HELPFILE} + ${HELP}/Factored.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7270 create Factored.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Factored.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19025,6 +19977,30 @@ ${HELP}/FactorisationOverPseudoAlgebraicClosureOfRationalNumber.help: \ "FactorisationOverPseudoAlgebraicClosureOfRationalNumber (FACTRN)" \ >>${HELPFILE} +${HELP}/Field.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Field.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Field.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Field.help + @cp ${HELP}/Field.help ${HELP}/FIELD.help + @${TANGLE} -R"Field.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Field.input + @echo "Field (FIELD)" >>${HELPFILE} + +${HELP}/FieldOfPrimeCharacteristic.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FieldOfPrimeCharacteristic.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FieldOfPrimeCharacteristic.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FieldOfPrimeCharacteristic.help + @cp ${HELP}/FieldOfPrimeCharacteristic.help ${HELP}/FPC.help + @${TANGLE} -R"FieldOfPrimeCharacteristic.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FieldOfPrimeCharacteristic.input + @echo "FieldOfPrimeCharacteristic (FPC)" >>${HELPFILE} + ${HELP}/File.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7290 create File.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"File.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19034,6 +20010,18 @@ ${HELP}/File.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/File.input @echo "File (FILE)" >>${HELPFILE} +${HELP}/FileCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FileCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FileCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FileCategory.help + @cp ${HELP}/FileCategory.help ${HELP}/FILECAT.help + @${TANGLE} -R"FileCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FileCategory.input + @echo "FileCategory (FILECAT)" >>${HELPFILE} + ${HELP}/FileName.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7300 create FileName.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"FileName.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19043,6 +20031,78 @@ ${HELP}/FileName.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/FileName.input @echo "FileName (FNAME)" >>${HELPFILE} +${HELP}/FileNameCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FileNameCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FileNameCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FileNameCategory.help + @cp ${HELP}/FileNameCategory.help ${HELP}/FNCAT.help + @${TANGLE} -R"FileNameCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FileNameCategory.input + @echo "FileNameCategory (FNCAT)" >>${HELPFILE} + +${HELP}/Finite.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Finite.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Finite.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Finite.help + @cp ${HELP}/Finite.help ${HELP}/FINITE.help + @${TANGLE} -R"Finite.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Finite.input + @echo "Finite (FINITE)" >>${HELPFILE} + +${HELP}/FiniteAbelianMonoidRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteAbelianMonoidRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteAbelianMonoidRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteAbelianMonoidRing.help + @cp ${HELP}/FiniteAbelianMonoidRing.help ${HELP}/FAMR.help + @${TANGLE} -R"FiniteAbelianMonoidRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteAbelianMonoidRing.input + @echo "FiniteAbelianMonoidRing (FAMR)" >>${HELPFILE} + +${HELP}/FiniteAlgebraicExtensionField.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteAlgebraicExtensionField.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteAlgebraicExtensionField.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteAlgebraicExtensionField.help + @cp ${HELP}/FiniteAlgebraicExtensionField.help ${HELP}/FAXF.help + @${TANGLE} -R"FiniteAlgebraicExtensionField.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteAlgebraicExtensionField.input + @echo "FiniteAlgebraicExtensionField (FAXF)" >>${HELPFILE} + +${HELP}/FiniteDivisorCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteDivisorCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteDivisorCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteDivisorCategory.help + @cp ${HELP}/FiniteDivisorCategory.help ${HELP}/FDIVCAT.help + @${TANGLE} -R"FiniteDivisorCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteDivisorCategory.input + @echo "FiniteDivisorCategory (FDIVCAT)" >>${HELPFILE} + +${HELP}/FiniteFieldCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteFieldCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteFieldCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteFieldCategory.help + @cp ${HELP}/FiniteFieldCategory.help ${HELP}/FFIELDC.help + @${TANGLE} -R"FiniteFieldCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteFieldCategory.input + @echo "FiniteFieldCategory (FFIELDC)" >>${HELPFILE} + ${HELP}/FiniteFieldFactorizationWithSizeParseBySideEffect.help: \ ${BOOKS}/bookvol10.4.pamphlet @echo 7303 create \ @@ -19072,6 +20132,54 @@ ${HELP}/FiniteFieldSquareFreeDecomposition.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/FiniteFieldSquareFreeDecomposition.input @echo "FiniteFieldSquareFreeDecomposition (FFSQFR)" >>${HELPFILE} +${HELP}/FiniteLinearAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteLinearAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteLinearAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteLinearAggregate.help + @cp ${HELP}/FiniteLinearAggregate.help ${HELP}/FLAGG.help + @${TANGLE} -R"FiniteLinearAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteLinearAggregate.input + @echo "FiniteLinearAggregate (FLAGG)" >>${HELPFILE} + +${HELP}/FiniteRankAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteRankAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteRankAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteRankAlgebra.help + @cp ${HELP}/FiniteRankAlgebra.help ${HELP}/FINRALG.help + @${TANGLE} -R"FiniteRankAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteRankAlgebra.input + @echo "FiniteRankAlgebra (FINRALG)" >>${HELPFILE} + +${HELP}/FiniteRankNonAssociativeAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteRankNonAssociativeAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteRankNonAssociativeAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteRankNonAssociativeAlgebra.help + @cp ${HELP}/FiniteRankNonAssociativeAlgebra.help ${HELP}/FINAALG.help + @${TANGLE} -R"FiniteRankNonAssociativeAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteRankNonAssociativeAlgebra.input + @echo "FiniteRankNonAssociativeAlgebra (FINAALG)" >>${HELPFILE} + +${HELP}/FiniteSetAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FiniteSetAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FiniteSetAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FiniteSetAggregate.help + @cp ${HELP}/FiniteSetAggregate.help ${HELP}/FSAGG.help + @${TANGLE} -R"FiniteSetAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FiniteSetAggregate.input + @echo "FiniteSetAggregate (FSAGG)" >>${HELPFILE} + ${HELP}/FlexibleArray.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7310 create FlexibleArray.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"FlexibleArray.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19090,6 +20198,102 @@ ${HELP}/Float.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Float.input @echo "Float (FLOAT)" >>${HELPFILE} +${HELP}/FloatingPointSystem.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FloatingPointSystem.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FloatingPointSystem.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FloatingPointSystem.help + @cp ${HELP}/FloatingPointSystem.help ${HELP}/FPS.help + @${TANGLE} -R"FloatingPointSystem.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FloatingPointSystem.input + @echo "FloatingPointSystem (FPS)" >>${HELPFILE} + +${HELP}/FortranFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranFunctionCategory.help + @cp ${HELP}/FortranFunctionCategory.help ${HELP}/FORFN.help + @${TANGLE} -R"FortranFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranFunctionCategory.input + @echo "FortranFunctionCategory (FORFN)" >>${HELPFILE} + +${HELP}/FortranMachineTypeCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranMachineTypeCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranMachineTypeCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranMachineTypeCategory.help + @cp ${HELP}/FortranMachineTypeCategory.help ${HELP}/FMTC.help + @${TANGLE} -R"FortranMachineTypeCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranMachineTypeCategory.input + @echo "FortranMachineTypeCategory (FMTC)" >>${HELPFILE} + +${HELP}/FortranMatrixCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranMatrixCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranMatrixCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranMatrixCategory.help + @cp ${HELP}/FortranMatrixCategory.help ${HELP}/FMC.help + @${TANGLE} -R"FortranMatrixCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranMatrixCategory.input + @echo "FortranMatrixCategory (FMC)" >>${HELPFILE} + +${HELP}/FortranMatrixFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranMatrixFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranMatrixFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranMatrixFunctionCategory.help + @cp ${HELP}/FortranMatrixFunctionCategory.help ${HELP}/FMFUN.help + @${TANGLE} -R"FortranMatrixFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranMatrixFunctionCategory.input + @echo "FortranMatrixFunctionCategory (FMFUN)" >>${HELPFILE} + +${HELP}/FortranProgramCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranProgramCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranProgramCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranProgramCategory.help + @cp ${HELP}/FortranProgramCategory.help ${HELP}/FORTCAT.help + @${TANGLE} -R"FortranProgramCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranProgramCategory.input + @echo "FortranProgramCategory (FORTCAT)" >>${HELPFILE} + +${HELP}/FortranVectorCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranVectorCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranVectorCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranVectorCategory.help + @cp ${HELP}/FortranVectorCategory.help ${HELP}/FVC.help + @${TANGLE} -R"FortranVectorCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranVectorCategory.input + @echo "FortranVectorCategory (FVC)" >>${HELPFILE} + +${HELP}/FortranVectorFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FortranVectorFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FortranVectorFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FortranVectorFunctionCategory.help + @cp ${HELP}/FortranVectorFunctionCategory.help ${HELP}/FVFUN.help + @${TANGLE} -R"FortranVectorFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FortranVectorFunctionCategory.input + @echo "FortranVectorFunctionCategory (FVFUN)" >>${HELPFILE} + ${HELP}/Fraction.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7330 create Fraction.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Fraction.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19099,6 +20303,66 @@ ${HELP}/Fraction.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Fraction.input @echo "Fraction (FRAC)" >>${HELPFILE} +${HELP}/FramedAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FramedAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FramedAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FramedAlgebra.help + @cp ${HELP}/FramedAlgebra.help ${HELP}/FRAMALG.help + @${TANGLE} -R"FramedAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FramedAlgebra.input + @echo "FramedAlgebra (FRAMALG)" >>${HELPFILE} + +${HELP}/FramedNonAssociativeAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FramedNonAssociativeAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FramedNonAssociativeAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FramedNonAssociativeAlgebra.help + @cp ${HELP}/FramedNonAssociativeAlgebra.help ${HELP}/FRNAALG.help + @${TANGLE} -R"FramedNonAssociativeAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FramedNonAssociativeAlgebra.input + @echo "FramedNonAssociativeAlgebra (FRNAALG)" >>${HELPFILE} + +${HELP}/FreeAbelianMonoidCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FreeAbelianMonoidCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FreeAbelianMonoidCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FreeAbelianMonoidCategory.help + @cp ${HELP}/FreeAbelianMonoidCategory.help ${HELP}/FAMONC.help + @${TANGLE} -R"FreeAbelianMonoidCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FreeAbelianMonoidCategory.input + @echo "FreeAbelianMonoidCategory (FAMONC)" >>${HELPFILE} + +${HELP}/FreeLieAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FreeLieAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FreeLieAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FreeLieAlgebra.help + @cp ${HELP}/FreeLieAlgebra.help ${HELP}/FLALG.help + @${TANGLE} -R"FreeLieAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FreeLieAlgebra.input + @echo "FreeLieAlgebra (FLALG)" >>${HELPFILE} + +${HELP}/FreeModuleCat.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FreeModuleCat.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FreeModuleCat.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FreeModuleCat.help + @cp ${HELP}/FreeModuleCat.help ${HELP}/FMCAT.help + @${TANGLE} -R"FreeModuleCat.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FreeModuleCat.input + @echo "FreeModuleCat (FMCAT)" >>${HELPFILE} + ${HELP}/FullPartialFractionExpansion.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7340 create FullPartialFractionExpansion.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19111,6 +20375,90 @@ ${HELP}/FullPartialFractionExpansion.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/FullPartialFractionExpansion.input @echo "FullPartialFractionExpansion (FPARFRAC)" >>${HELPFILE} +${HELP}/FullyEvalableOver.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FullyEvalableOver.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FullyEvalableOver.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FullyEvalableOver.help + @cp ${HELP}/FullyEvalableOver.help ${HELP}/FEVALAB.help + @${TANGLE} -R"FullyEvalableOver.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FullyEvalableOver.input + @echo "FullyEvalableOver (FEVALAB)" >>${HELPFILE} + +${HELP}/FullyLinearlyExplicitRingOver.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FullyLinearlyExplicitRingOver.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FullyLinearlyExplicitRingOver.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FullyLinearlyExplicitRingOver.help + @cp ${HELP}/FullyLinearlyExplicitRingOver.help ${HELP}/FLINEXP.help + @${TANGLE} -R"FullyLinearlyExplicitRingOver.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FullyLinearlyExplicitRingOver.input + @echo "FullyLinearlyExplicitRingOver (FLINEXP)" >>${HELPFILE} + +${HELP}/FullyPatternMatchable.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FullyPatternMatchable.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FullyPatternMatchable.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FullyPatternMatchable.help + @cp ${HELP}/FullyPatternMatchable.help ${HELP}/FPATMAB.help + @${TANGLE} -R"FullyPatternMatchable.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FullyPatternMatchable.input + @echo "FullyPatternMatchable (FPATMAB)" >>${HELPFILE} + +${HELP}/FullyRetractableTo.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FullyRetractableTo.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FullyRetractableTo.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FullyRetractableTo.help + @cp ${HELP}/FullyRetractableTo.help ${HELP}/FRETRCT.help + @${TANGLE} -R"FullyRetractableTo.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FullyRetractableTo.input + @echo "FullyRetractableTo (FRETRCT)" >>${HELPFILE} + +${HELP}/FunctionFieldCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FunctionFieldCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FunctionFieldCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FunctionFieldCategory.help + @cp ${HELP}/FunctionFieldCategory.help ${HELP}/FFCAT.help + @${TANGLE} -R"FunctionFieldCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FunctionFieldCategory.input + @echo "FunctionFieldCategory (FFCAT)" >>${HELPFILE} + +${HELP}/FunctionSpace.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create FunctionSpace.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"FunctionSpace.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/FunctionSpace.help + @cp ${HELP}/FunctionSpace.help ${HELP}/FS.help + @${TANGLE} -R"FunctionSpace.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/FunctionSpace.input + @echo "FunctionSpace (FS)" >>${HELPFILE} + +${HELP}/GcdDomain.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create GcdDomain.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"GcdDomain.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/GcdDomain.help + @cp ${HELP}/GcdDomain.help ${HELP}/GCDDOM.help + @${TANGLE} -R"GcdDomain.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/GcdDomain.input + @echo "GcdDomain (GCDDOM)" >>${HELPFILE} + ${HELP}/GeneralDistributedMultivariatePolynomial.help: \ ${BOOKS}/bookvol10.3.pamphlet @echo 7350 create GeneralDistributedMultivariatePolynomial.help \ @@ -19149,6 +20497,30 @@ ${HELP}/GeneralSparseTable.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/GeneralSparseTable.input @echo "GeneralSparseTable (GSTBL)" >>${HELPFILE} +${HELP}/GradedAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create GradedAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"GradedAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/GradedAlgebra.help + @cp ${HELP}/GradedAlgebra.help ${HELP}/GRALG.help + @${TANGLE} -R"GradedAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/GradedAlgebra.input + @echo "GradedAlgebra (GRALG)" >>${HELPFILE} + +${HELP}/GradedModule.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create GradedModule.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"GradedModule.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/GradedModule.help + @cp ${HELP}/GradedModule.help ${HELP}/GRMOD.help + @${TANGLE} -R"GradedModule.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/GradedModule.input + @echo "GradedModule (GRMOD)" >>${HELPFILE} + ${HELP}/GroebnerFactorizationPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7370 create GroebnerFactorizationPackage.help \ from ${BOOKS}/bookvol10.4.pamphlet @@ -19171,6 +20543,18 @@ ${HELP}/GroebnerPackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/GroebnerPackage.input @echo "GroebnerPackage (GB)" >>${HELPFILE} +${HELP}/Group.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Group.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Group.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Group.help + @cp ${HELP}/Group.help ${HELP}/GROUP.help + @${TANGLE} -R"Group.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Group.input + @echo "Group (GROUP)" >>${HELPFILE} + ${HELP}/Heap.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7390 create Heap.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Heap.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19191,6 +20575,18 @@ ${HELP}/HexadecimalExpansion.help: ${BOOKS}/bookvol10.3.pamphlet ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/HexadecimalExpansion.input @echo "HexadecimalExpansion (HEXADEC)" >>${HELPFILE} +${HELP}/HomogeneousAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create HomogeneousAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"HomogeneousAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/HomogeneousAggregate.help + @cp ${HELP}/HomogeneousAggregate.help ${HELP}/HOAGG.help + @${TANGLE} -R"HomogeneousAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/HomogeneousAggregate.input + @echo "HomogeneousAggregate (HOAGG)" >>${HELPFILE} + ${HELP}/HomogeneousDistributedMultivariatePolynomial.help: \ ${BOOKS}/bookvol10.3.pamphlet @echo 7410 create HomogeneousDistributedMultivariatePolynomial.help \ @@ -19206,6 +20602,30 @@ ${HELP}/HomogeneousDistributedMultivariatePolynomial.help: \ @echo "HomogeneousDistributedMultivariatePolynomial (HDMP)" \ >>${HELPFILE} +${HELP}/HyperbolicFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create HyperbolicFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"HyperbolicFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/HyperbolicFunctionCategory.help + @cp ${HELP}/HyperbolicFunctionCategory.help ${HELP}/HYPCAT.help + @${TANGLE} -R"HyperbolicFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/HyperbolicFunctionCategory.input + @echo "HyperbolicFunctionCategory (HYPCAT)" >>${HELPFILE} + +${HELP}/IndexedAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create IndexedAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"IndexedAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/IndexedAggregate.help + @cp ${HELP}/IndexedAggregate.help ${HELP}/IXAGG.help + @${TANGLE} -R"IndexedAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/IndexedAggregate.input + @echo "IndexedAggregate (IXAGG)" >>${HELPFILE} + ${HELP}/IndexedBits.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7415 create IndexedBits.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"IndexedBits.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19215,6 +20635,18 @@ ${HELP}/IndexedBits.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/IndexedBits.input @echo "IndexedBits (IBITS)" >>${HELPFILE} +${HELP}/IndexedDirectProductCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create IndexedDirectProductCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"IndexedDirectProductCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/IndexedDirectProductCategory.help + @cp ${HELP}/IndexedDirectProductCategory.help ${HELP}/IDPC.help + @${TANGLE} -R"IndexedDirectProductCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/IndexedDirectProductCategory.input + @echo "IndexedDirectProductCategory (IDPC)" >>${HELPFILE} + ${HELP}/InfClsPt.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7417 create InfClsPt.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19271,6 +20703,18 @@ ${HELP}/InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField.help: \ "InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField (INFCLSPS)" \ >>${HELPFILE} +${HELP}/InnerEvalable.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create InnerEvalable.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"InnerEvalable.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/InnerEvalable.help + @cp ${HELP}/InnerEvalable.help ${HELP}/IEVALAB.help + @${TANGLE} -R"InnerEvalable.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/InnerEvalable.input + @echo "InnerEvalable (IEVALAB)" >>${HELPFILE} + ${HELP}/Integer.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7425 create Integer.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Integer.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19304,6 +20748,18 @@ ${HELP}/IntegerLinearDependence.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/IntegerLinearDependence.input @echo "IntegerLinearDependence (ZLINDEP)" >>${HELPFILE} +${HELP}/IntegerNumberSystem.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create IntegerNumberSystem.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"IntegerNumberSystem.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/IntegerNumberSystem.help + @cp ${HELP}/IntegerNumberSystem.help ${HELP}/INS.help + @${TANGLE} -R"IntegerNumberSystem.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/IntegerNumberSystem.input + @echo "IntegerNumberSystem (INS)" >>${HELPFILE} + ${HELP}/IntegerNumberTheoryFunctions.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7450 create IntegerNumberTheoryFunctions.help \ from ${BOOKS}/bookvol10.4.pamphlet @@ -19317,6 +20773,18 @@ ${HELP}/IntegerNumberTheoryFunctions.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/IntegerNumberTheoryFunctions.input @echo "IntegerNumberTheoryFunctions (INTHEORY)" >>${HELPFILE} +${HELP}/IntegralDomain.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create IntegralDomain.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"IntegralDomain.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/IntegralDomain.help + @cp ${HELP}/IntegralDomain.help ${HELP}/INTDOM.help + @${TANGLE} -R"IntegralDomain.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/IntegralDomain.input + @echo "IntegralDomain (INTDOM)" >>${HELPFILE} + ${HELP}/InterfaceGroebnerPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7455 create InterfaceGroebnerPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -19362,6 +20830,18 @@ ${HELP}/Interval.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Interval.input @echo "Interval (INTRVL)" >>${HELPFILE} +${HELP}/IntervalCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create IntervalCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"IntervalCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/IntervalCategory.help + @cp ${HELP}/IntervalCategory.help ${HELP}/INTCAT.help + @${TANGLE} -R"IntervalCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/IntervalCategory.input + @echo "IntervalCategory (INTCAT)" >>${HELPFILE} + ${HELP}/Kernel.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7460 create Kernel.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Kernel.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19381,6 +20861,30 @@ ${HELP}/KeyedAccessFile.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/KeyedAccessFile.input @echo "KeyedAccessFile (KAFILE)" >>${HELPFILE} +${HELP}/KeyedDictionary.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create KeyedDictionary.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"KeyedDictionary.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/KeyedDictionary.help + @cp ${HELP}/KeyedDictionary.help ${HELP}/KDAGG.help + @${TANGLE} -R"KeyedDictionary.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/KeyedDictionary.input + @echo "KeyedDictionary (KDAGG)" >>${HELPFILE} + +${HELP}/LazyStreamAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LazyStreamAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LazyStreamAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LazyStreamAggregate.help + @cp ${HELP}/LazyStreamAggregate.help ${HELP}/LZSTAGG.help + @${TANGLE} -R"LazyStreamAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LazyStreamAggregate.input + @echo "LazyStreamAggregate (LZSTAGG)" >>${HELPFILE} + ${HELP}/LazardSetSolvingPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7480 create LazardSetSolvingPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -19393,6 +20897,30 @@ ${HELP}/LazardSetSolvingPackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/LazardSetSolvingPackage.input @echo "LazardSetSolvingPackage (LAZM3PK)" >>${HELPFILE} +${HELP}/LeftAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LeftAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LeftAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LeftAlgebra.help + @cp ${HELP}/LeftAlgebra.help ${HELP}/LALG.help + @${TANGLE} -R"LeftAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LeftAlgebra.input + @echo "LeftAlgebra (LALG)" >>${HELPFILE} + +${HELP}/LeftModule.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LeftModule.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LeftModule.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LeftModule.help + @cp ${HELP}/LeftModule.help ${HELP}/LMODULE.help + @${TANGLE} -R"LeftModule.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LeftModule.input + @echo "LeftModule (LMODULE)" >>${HELPFILE} + ${HELP}/LexTriangularPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7490 create LexTriangularPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -19414,6 +20942,18 @@ ${HELP}/Library.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Library.input @echo "Library (LIB)" >>${HELPFILE} +${HELP}/LieAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LieAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LieAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LieAlgebra.help + @cp ${HELP}/LieAlgebra.help ${HELP}/LIECAT.help + @${TANGLE} -R"LieAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LieAlgebra.input + @echo "LieAlgebra (LIECAT)" >>${HELPFILE} + ${HELP}/LieExponentials.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7510 create LieExponentials.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19438,6 +20978,30 @@ ${HELP}/LiePolynomial.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/LiePolynomial.input @echo "LiePolynomial (LPOLY)" >>${HELPFILE} +${HELP}/LinearlyExplicitRingOver.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LinearlyExplicitRingOver.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LinearlyExplicitRingOver.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LinearlyExplicitRingOver.help + @cp ${HELP}/LinearlyExplicitRingOver.help ${HELP}/LINEXP.help + @${TANGLE} -R"LinearlyExplicitRingOver.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LinearlyExplicitRingOver.input + @echo "LinearlyExplicitRingOver (LINEXP)" >>${HELPFILE} + +${HELP}/LinearAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LinearAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LinearAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LinearAggregate.help + @cp ${HELP}/LinearAggregate.help ${HELP}/LNAGG.help + @${TANGLE} -R"LinearAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LinearAggregate.input + @echo "LinearAggregate (LNAGG)" >>${HELPFILE} + ${HELP}/LinearOrdinaryDifferentialOperator.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7530 create LinearOrdinaryDifferentialOperator.help \ from ${BOOKS}/bookvol10.3.pamphlet @@ -19476,6 +21040,21 @@ ${HELP}/LinearOrdinaryDifferentialOperator2.help: \ >${INPUT}/LinearOrdinaryDifferentialOperator2.input @echo "LinearOrdinaryDifferentialOperator2 (LODO2)" >>${HELPFILE} +${HELP}/LinearOrdinaryDifferentialOperatorCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LinearOrdinaryDifferentialOperatorCategory.help \ + from ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LinearOrdinaryDifferentialOperatorCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LinearOrdinaryDifferentialOperatorCategory.help + @cp ${HELP}/LinearOrdinaryDifferentialOperatorCategory.help \ + ${HELP}/LODOCAT.help + @${TANGLE} -R"LinearOrdinaryDifferentialOperatorCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LinearOrdinaryDifferentialOperatorCategory.input + @echo "LinearOrdinaryDifferentialOperatorCategory (LODOCAT)" \ + >>${HELPFILE} + ${HELP}/LinearSystemFromPowerSeriesPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7555 create LinearSystemFromPowerSeriesPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -19489,6 +21068,30 @@ ${HELP}/LinearSystemFromPowerSeriesPackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/LinearSystemFromPowerSeriesPackage.input @echo "LinearSystemFromPowerSeriesPackage (LISYSER)" >>${HELPFILE} +${HELP}/ListAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ListAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ListAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ListAggregate.help + @cp ${HELP}/ListAggregate.help ${HELP}/LSAGG.help + @${TANGLE} -R"ListAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ListAggregate.input + @echo "ListAggregate (LSAGG)" >>${HELPFILE} + +${HELP}/LiouvillianFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create LiouvillianFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"LiouvillianFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/LiouvillianFunctionCategory.help + @cp ${HELP}/LiouvillianFunctionCategory.help ${HELP}/LFCAT.help + @${TANGLE} -R"LiouvillianFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/LiouvillianFunctionCategory.input + @echo "LiouvillianFunctionCategory (LFCAT)" >>${HELPFILE} + ${HELP}/List.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7560 create List.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"List.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19534,6 +21137,18 @@ ${HELP}/LocalPowerSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet >${INPUT}/LocalPowerSeriesCategory.input @echo "LocalPowerSeriesCategory (LOCPOWC)" >>${HELPFILE} +${HELP}/Logic.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Logic.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Logic.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Logic.help + @cp ${HELP}/Logic.help ${HELP}/LOGIC.help + @${TANGLE} -R"Logic.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Logic.input + @echo "Logic (LOGIC)" >>${HELPFILE} + ${HELP}/LyndonWord.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7570 create LyndonWord.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19625,6 +21240,90 @@ ${HELP}/MatrixCategory.help: ${BOOKS}/bookvol10.2.pamphlet >${INPUT}/MatrixCategory.input @echo "MatrixCategory (MATCAT)" >>${HELPFILE} +${HELP}/Module.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Module.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Module.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Module.help + @cp ${HELP}/Module.help ${HELP}/MODULE.help + @${TANGLE} -R"Module.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Module.input + @echo "Module (MODULE)" >>${HELPFILE} + +${HELP}/Monad.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Monad.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Monad.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Monad.help + @cp ${HELP}/Monad.help ${HELP}/MONAD.help + @${TANGLE} -R"Monad.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Monad.input + @echo "Monad (MONAD)" >>${HELPFILE} + +${HELP}/MonadWithUnit.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create MonadWithUnit.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"MonadWithUnit.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/MonadWithUnit.help + @cp ${HELP}/MonadWithUnit.help ${HELP}/MONADWU.help + @${TANGLE} -R"MonadWithUnit.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/MonadWithUnit.input + @echo "MonadWithUnit (MONADWU)" >>${HELPFILE} + +${HELP}/MonogenicAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create MonogenicAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"MonogenicAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/MonogenicAlgebra.help + @cp ${HELP}/MonogenicAlgebra.help ${HELP}/MONOGEN.help + @${TANGLE} -R"MonogenicAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/MonogenicAlgebra.input + @echo "MonogenicAlgebra (MONOGEN)" >>${HELPFILE} + +${HELP}/MonogenicLinearOperator.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create MonogenicLinearOperator.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"MonogenicLinearOperator.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/MonogenicLinearOperator.help + @cp ${HELP}/MonogenicLinearOperator.help ${HELP}/MLO.help + @${TANGLE} -R"MonogenicLinearOperator.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/MonogenicLinearOperator.input + @echo "MonogenicLinearOperator (MLO)" >>${HELPFILE} + +${HELP}/Monoid.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Monoid.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Monoid.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Monoid.help + @cp ${HELP}/Monoid.help ${HELP}/MONOID.help + @${TANGLE} -R"Monoid.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Monoid.input + @echo "Monoid (MONOID)" >>${HELPFILE} + +${HELP}/MultiDictionary.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create MultiDictionary.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"MultiDictionary.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/MultiDictionary.help + @cp ${HELP}/MultiDictionary.help ${HELP}/MDAGG.help + @${TANGLE} -R"MultiDictionary.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/MultiDictionary.input + @echo "MultiDictionary (MDAGG)" >>${HELPFILE} + ${HELP}/Multiset.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7650 create Multiset.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Multiset.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19634,6 +21333,18 @@ ${HELP}/Multiset.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Multiset.input @echo "Multiset (MSET)" >>${HELPFILE} +${HELP}/MultisetAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create MultisetAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"MultisetAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/MultisetAggregate.help + @cp ${HELP}/MultisetAggregate.help ${HELP}/MSETAGG.help + @${TANGLE} -R"MultisetAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/MultisetAggregate.input + @echo "MultisetAggregate (MSETAGG)" >>${HELPFILE} + ${HELP}/MultivariatePolynomial.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7660 create MultivariatePolynomial.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19646,6 +21357,18 @@ ${HELP}/MultivariatePolynomial.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/MultivariatePolynomial.input @echo "MultivariatePolynomial (MPOLY)" >>${HELPFILE} +${HELP}/MultivariateTaylorSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create MultivariateTaylorSeriesCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"MultivariateTaylorSeriesCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/MultivariateTaylorSeriesCategory.help + @cp ${HELP}/MultivariateTaylorSeriesCategory.help ${HELP}/MTSCAT.help + @${TANGLE} -R"MultivariateTaylorSeriesCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/MultivariateTaylorSeriesCategory.input + @echo "MultivariateTaylorSeriesCategory (MTSCAT)" >>${HELPFILE} + ${HELP}/NagEigenPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7670 create NagEigenPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -19797,6 +21520,42 @@ ${HELP}/NewtonPolygon.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/NewtonPolygon.input @echo "NewtonPolygon (NPOLYGON)" >>${HELPFILE} +${HELP}/NonAssociativeAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create NonAssociativeAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"NonAssociativeAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/NonAssociativeAlgebra.help + @cp ${HELP}/NonAssociativeAlgebra.help ${HELP}/NAALG.help + @${TANGLE} -R"NonAssociativeAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/NonAssociativeAlgebra.input + @echo "NonAssociativeAlgebra (NAALG)" >>${HELPFILE} + +${HELP}/NonAssociativeRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create NonAssociativeRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"NonAssociativeRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/NonAssociativeRing.help + @cp ${HELP}/NonAssociativeRing.help ${HELP}/NASRING.help + @${TANGLE} -R"NonAssociativeRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/NonAssociativeRing.input + @echo "NonAssociativeRing (NASRING)" >>${HELPFILE} + +${HELP}/NonAssociativeRng.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create NonAssociativeRng.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"NonAssociativeRng.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/NonAssociativeRng.help + @cp ${HELP}/NonAssociativeRng.help ${HELP}/NARNG.help + @${TANGLE} -R"NonAssociativeRng.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/NonAssociativeRng.input + @echo "NonAssociativeRng (NARNG)" >>${HELPFILE} + ${HELP}/None.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7810 create None.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"None.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19806,6 +21565,18 @@ ${HELP}/None.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/None.input @echo "None (NONE)" >>${HELPFILE} +${HELP}/NormalizedTriangularSetCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create NormalizedTriangularSetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"NormalizedTriangularSetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/NormalizedTriangularSetCategory.help + @cp ${HELP}/NormalizedTriangularSetCategory.help ${HELP}/NTSCAT.help + @${TANGLE} -R"NormalizedTriangularSetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/NormalizedTriangularSetCategory.input + @echo "NormalizedTriangularSetCategory (NTSCAT)" >>${HELPFILE} + ${HELP}/NottinghamGroup.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7820 create NottinghamGroup.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19816,6 +21587,30 @@ ${HELP}/NottinghamGroup.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/NottinghamGroup.input @echo "NottinghamGroup (NOTTING)" >>${HELPFILE} +${HELP}/NumericalIntegrationCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create NumericalIntegrationCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"NumericalIntegrationCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/NumericalIntegrationCategory.help + @cp ${HELP}/NumericalIntegrationCategory.help ${HELP}/NUMINT.help + @${TANGLE} -R"NumericalIntegrationCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/NumericalIntegrationCategory.input + @echo "NumericalIntegrationCategory (NUMINT)" >>${HELPFILE} + +${HELP}/NumericalOptimizationCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create NumericalOptimizationCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"NumericalOptimizationCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/NumericalOptimizationCategory.help + @cp ${HELP}/NumericalOptimizationCategory.help ${HELP}/OPTCAT.help + @${TANGLE} -R"NumericalOptimizationCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/NumericalOptimizationCategory.input + @echo "NumericalOptimizationCategory (OPTCAT)" >>${HELPFILE} + ${HELP}/Octonion.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7830 create Octonion.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Octonion.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19825,6 +21620,18 @@ ${HELP}/Octonion.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Octonion.input @echo "Octonion (OCT)" >>${HELPFILE} +${HELP}/OctonionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OctonionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OctonionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OctonionCategory.help + @cp ${HELP}/OctonionCategory.help ${HELP}/OC.help + @${TANGLE} -R"OctonionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OctonionCategory.input + @echo "OctonionCategory (OC)" >>${HELPFILE} + ${HELP}/OneDimensionalArray.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7840 create OneDimensionalArray.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19836,6 +21643,30 @@ ${HELP}/OneDimensionalArray.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/OneDimensionalArray.input @echo "OneDimensionalArray (ARRAY1)" >>${HELPFILE} +${HELP}/OneDimensionalArrayAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OneDimensionalArrayAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OneDimensionalArrayAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OneDimensionalArrayAggregate.help + @cp ${HELP}/OneDimensionalArrayAggregate.help ${HELP}/A1AGG.help + @${TANGLE} -R"OneDimensionalArrayAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OneDimensionalArrayAggregate.input + @echo "OneDimensionalArrayAggregate (A1AGG)" >>${HELPFILE} + +${HELP}/OpenMath.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OpenMath.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OpenMath.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OpenMath.help + @cp ${HELP}/OpenMath.help ${HELP}/OM.help + @${TANGLE} -R"OpenMath.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OpenMath.input + @echo "OpenMath (OM)" >>${HELPFILE} + ${HELP}/Operator.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7850 create Operator.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Operator.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -19845,6 +21676,78 @@ ${HELP}/Operator.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Operator.input @echo "Operator (OP)" >>${HELPFILE} +${HELP}/OrderedAbelianGroup.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedAbelianGroup.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedAbelianGroup.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedAbelianGroup.help + @cp ${HELP}/OrderedAbelianGroup.help ${HELP}/OAGROUP.help + @${TANGLE} -R"OrderedAbelianGroup.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedAbelianGroup.input + @echo "OrderedAbelianGroup (OAGROUP)" >>${HELPFILE} + +${HELP}/OrderedAbelianMonoid.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedAbelianMonoid.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedAbelianMonoid.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedAbelianMonoid.help + @cp ${HELP}/OrderedAbelianMonoid.help ${HELP}/OAMON.help + @${TANGLE} -R"OrderedAbelianMonoid.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedAbelianMonoid.input + @echo "OrderedAbelianMonoid (OAMON)" >>${HELPFILE} + +${HELP}/OrderedAbelianMonoidSup.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedAbelianMonoidSup.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedAbelianMonoidSup.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedAbelianMonoidSup.help + @cp ${HELP}/OrderedAbelianMonoidSup.help ${HELP}/OAMONS.help + @${TANGLE} -R"OrderedAbelianMonoidSup.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedAbelianMonoidSup.input + @echo "OrderedAbelianMonoidSup (OAMONS)" >>${HELPFILE} + +${HELP}/OrderedAbelianSemiGroup.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedAbelianSemiGroup.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedAbelianSemiGroup.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedAbelianSemiGroup.help + @cp ${HELP}/OrderedAbelianSemiGroup.help ${HELP}/OASGP.help + @${TANGLE} -R"OrderedAbelianSemiGroup.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedAbelianSemiGroup.input + @echo "OrderedAbelianSemiGroup (OASGP)" >>${HELPFILE} + +${HELP}/OrderedCancellationAbelianMonoid.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedCancellationAbelianMonoid.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedCancellationAbelianMonoid.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedCancellationAbelianMonoid.help + @cp ${HELP}/OrderedCancellationAbelianMonoid.help ${HELP}/OCAMON.help + @${TANGLE} -R"OrderedCancellationAbelianMonoid.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedCancellationAbelianMonoid.input + @echo "OrderedCancellationAbelianMonoid (OCAMON)" >>${HELPFILE} + +${HELP}/OrderedFinite.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedFinite.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedFinite.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedFinite.help + @cp ${HELP}/OrderedFinite.help ${HELP}/ORDFIN.help + @${TANGLE} -R"OrderedFinite.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedFinite.input + @echo "OrderedFinite (ORDFIN)" >>${HELPFILE} + ${HELP}/OrderedFreeMonoid.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7855 create OrderedFreeMonoid.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19855,6 +21758,66 @@ ${HELP}/OrderedFreeMonoid.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/OrderedFreeMonoid.input @echo "OrderedFreeMonoid (OFMONOID)" >>${HELPFILE} +${HELP}/OrderedIntegralDomain.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedIntegralDomain.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedIntegralDomain.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedIntegralDomain.help + @cp ${HELP}/OrderedIntegralDomain.help ${HELP}/OINTDOM.help + @${TANGLE} -R"OrderedIntegralDomain.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedIntegralDomain.input + @echo "OrderedIntegralDomain (OINTDOM)" >>${HELPFILE} + +${HELP}/OrderedMonoid.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedMonoid.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedMonoid.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedMonoid.help + @cp ${HELP}/OrderedMonoid.help ${HELP}/ORDMON.help + @${TANGLE} -R"OrderedMonoid.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedMonoid.input + @echo "OrderedMonoid (ORDMON)" >>${HELPFILE} + +${HELP}/OrderedMultisetAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedMultisetAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedMultisetAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedMultisetAggregate.help + @cp ${HELP}/OrderedMultisetAggregate.help ${HELP}/OMSAGG.help + @${TANGLE} -R"OrderedMultisetAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedMultisetAggregate.input + @echo "OrderedMultisetAggregate (OMSAGG)" >>${HELPFILE} + +${HELP}/OrderedRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedRing.help + @cp ${HELP}/OrderedRing.help ${HELP}/ORDRING.help + @${TANGLE} -R"OrderedRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedRing.input + @echo "OrderedRing (ORDRING)" >>${HELPFILE} + +${HELP}/OrderedSet.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create OrderedSet.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrderedSet.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrderedSet.help + @cp ${HELP}/OrderedSet.help ${HELP}/ORDSET.help + @${TANGLE} -R"OrderedSet.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrderedSet.input + @echo "OrderedSet (ORDSET)" >>${HELPFILE} + ${HELP}/OrderedVariableList.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7860 create OrderedVariableList.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19879,6 +21842,22 @@ ${HELP}/OrderlyDifferentialPolynomial.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/OrderlyDifferentialPolynomial.input @echo "OrderlyDifferentialPolynomial (ODPOL)" >>${HELPFILE} +${HELP}/OrdinaryDifferentialEquationsSolverCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create \ + OrdinaryDifferentialEquationsSolverCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"OrdinaryDifferentialEquationsSolverCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/OrdinaryDifferentialEquationsSolverCategory.help + @cp ${HELP}/OrdinaryDifferentialEquationsSolverCategory.help \ + ${HELP}/ODECAT.help + @${TANGLE} -R"OrdinaryDifferentialEquationsSolverCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/OrdinaryDifferentialEquationsSolverCategory.input + @echo "OrdinaryDifferentialEquationsSolverCategory (ODECAT)" \ + >>${HELPFILE} + ${HELP}/PackageForAlgebraicFunctionField.help: \ ${BOOKS}/bookvol10.4.pamphlet @echo 7875 make PackageForAlgebraicFunctionField.help \ @@ -19919,6 +21898,18 @@ ${HELP}/PackageForPoly.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/PackageForPoly.input @echo "PackageForPoly (PFORP)" >>${HELPFILE} +${HELP}/PAdicIntegerCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PAdicIntegerCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PAdicIntegerCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PAdicIntegerCategory.help + @cp ${HELP}/PAdicIntegerCategory.help ${HELP}/PADICCT.help + @${TANGLE} -R"PAdicIntegerCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PAdicIntegerCategory.input + @echo "PAdicIntegerCategory (PADICCT)" >>${HELPFILE} + ${HELP}/ParametrizationPackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7882 create ParametrizationPackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -19931,6 +21922,34 @@ ${HELP}/ParametrizationPackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/ParametrizationPackage.input @echo "ParametrizationPackage (PARAMP)" >>${HELPFILE} +${HELP}/PartialDifferentialEquationsSolverCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create \ + PartialDifferentialEquationsSolverCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PartialDifferentialEquationsSolverCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PartialDifferentialEquationsSolverCategory.help + @cp ${HELP}/PartialDifferentialEquationsSolverCategory.help \ + ${HELP}/PDECAT.help + @${TANGLE} -R"PartialDifferentialEquationsSolverCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PartialDifferentialEquationsSolverCategory.input + @echo "PartialDifferentialEquationsSolverCategory (PDECAT)" \ + >>${HELPFILE} + +${HELP}/PartialDifferentialRing.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PartialDifferentialRing.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PartialDifferentialRing.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PartialDifferentialRing.help + @cp ${HELP}/PartialDifferentialRing.help ${HELP}/PDRING.help + @${TANGLE} -R"PartialDifferentialRing.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PartialDifferentialRing.input + @echo "PartialDifferentialRing (PDRING)" >>${HELPFILE} + ${HELP}/PartialFraction.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7884 create PartialFraction.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -19953,6 +21972,42 @@ ${HELP}/PartialFractionPackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/PartialFractionPackage.input @echo "PartialFractionPackage (PFRPAC)" >>${HELPFILE} +${HELP}/PartialTranscendentalFunctions.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PartialTranscendentalFunctions.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PartialTranscendentalFunctions.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PartialTranscendentalFunctions.help + @cp ${HELP}/PartialTranscendentalFunctions.help ${HELP}/PTRANFN.help + @${TANGLE} -R"PartialTranscendentalFunctions.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PartialTranscendentalFunctions.input + @echo "PartialTranscendentalFunctions (PTRANFN)" >>${HELPFILE} + +${HELP}/Patternable.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Patternable.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Patternable.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Patternable.help + @cp ${HELP}/Patternable.help ${HELP}/PATAB.help + @${TANGLE} -R"Patternable.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Patternable.input + @echo "Patternable (PATAB)" >>${HELPFILE} + +${HELP}/PatternMatchable.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PatternMatchable.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PatternMatchable.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PatternMatchable.help + @cp ${HELP}/PatternMatchable.help ${HELP}/PATMAB.help + @${TANGLE} -R"PatternMatchable.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PatternMatchable.input + @echo "PatternMatchable (PATMAB)" >>${HELPFILE} + ${HELP}/Permanent.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7890 create Permanent.help from ${BOOKS}/bookvol10.4.pamphlet @${TANGLE} -R"Permanent.help" ${BOOKS}/bookvol10.4.pamphlet \ @@ -19971,6 +22026,18 @@ ${HELP}/Permutation.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Permutation.input @echo "Permutation (PERM)" >>${HELPFILE} +${HELP}/PermutationCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PermutationCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PermutationCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PermutationCategory.help + @cp ${HELP}/PermutationCategory.help ${HELP}/PERMCAT.help + @${TANGLE} -R"PermutationCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PermutationCategory.input + @echo "PermutationCategory (PERMCAT)" >>${HELPFILE} + ${HELP}/Places.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7905 create Places.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20041,6 +22108,42 @@ ${HELP}/Plot.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Plot.input @echo "Plot (PLOT)" >>${HELPFILE} +${HELP}/PlottablePlaneCurveCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PlottablePlaneCurveCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PlottablePlaneCurveCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PlottablePlaneCurveCategory.help + @cp ${HELP}/PlottablePlaneCurveCategory.help ${HELP}/PPCURVE.help + @${TANGLE} -R"PlottablePlaneCurveCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PlottablePlaneCurveCategory.input + @echo "PlottablePlaneCurveCategory (PPCURVE)" >>${HELPFILE} + +${HELP}/PlottableSpaceCurveCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PlottableSpaceCurveCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PlottableSpaceCurveCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PlottableSpaceCurveCategory.help + @cp ${HELP}/PlottableSpaceCurveCategory.help ${HELP}/PSCURVE.help + @${TANGLE} -R"PlottableSpaceCurveCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PlottableSpaceCurveCategory.input + @echo "PlottableSpaceCurveCategory (PSCURVE)" >>${HELPFILE} + +${HELP}/PointCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PointCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PointCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PointCategory.help + @cp ${HELP}/PointCategory.help ${HELP}/PTCAT.help + @${TANGLE} -R"PointCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PointCategory.input + @echo "PointCategory (PTCAT)" >>${HELPFILE} + ${HELP}/Polynomial.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7930 create Polynomial.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Polynomial.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20050,6 +22153,30 @@ ${HELP}/Polynomial.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Polynomial.input @echo "Polynomial (POLY)" >>${HELPFILE} +${HELP}/PolynomialCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PolynomialCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PolynomialCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PolynomialCategory.help + @cp ${HELP}/PolynomialCategory.help ${HELP}/POLYCAT.help + @${TANGLE} -R"PolynomialCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PolynomialCategory.input + @echo "PolynomialCategory (POLYCAT)" >>${HELPFILE} + +${HELP}/PolynomialFactorizationExplicit.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PolynomialFactorizationExplicit.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PolynomialFactorizationExplicit.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PolynomialFactorizationExplicit.help + @cp ${HELP}/PolynomialFactorizationExplicit.help ${HELP}/PFECAT.help + @${TANGLE} -R"PolynomialFactorizationExplicit.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PolynomialFactorizationExplicit.input + @echo "PolynomialFactorizationExplicit (PFECAT)" >>${HELPFILE} + ${HELP}/PolynomialPackageForCurve.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7933 create PolynomialPackageForCurve.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -20062,6 +22189,66 @@ ${HELP}/PolynomialPackageForCurve.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/PolynomialPackageForCurve.input @echo "PolynomialPackageForCurve (PLPKCRV)" >>${HELPFILE} +${HELP}/PolynomialSetCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PolynomialSetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PolynomialSetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PolynomialSetCategory.help + @cp ${HELP}/PolynomialSetCategory.help ${HELP}/PSETCAT.help + @${TANGLE} -R"PolynomialSetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PolynomialSetCategory.input + @echo "PolynomialSetCategory (PSETCAT)" >>${HELPFILE} + +${HELP}/PowerSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PowerSeriesCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PowerSeriesCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PowerSeriesCategory.help + @cp ${HELP}/PowerSeriesCategory.help ${HELP}/PSCAT.help + @${TANGLE} -R"PowerSeriesCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PowerSeriesCategory.input + @echo "PowerSeriesCategory (PSCAT)" >>${HELPFILE} + +${HELP}/PrimitiveFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PrimitiveFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PrimitiveFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PrimitiveFunctionCategory.help + @cp ${HELP}/PrimitiveFunctionCategory.help ${HELP}/PRIMCAT.help + @${TANGLE} -R"PrimitiveFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PrimitiveFunctionCategory.input + @echo "PrimitiveFunctionCategory (PRIMCAT)" >>${HELPFILE} + +${HELP}/PrincipalIdealDomain.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PrincipalIdealDomain.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PrincipalIdealDomain.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PrincipalIdealDomain.help + @cp ${HELP}/PrincipalIdealDomain.help ${HELP}/PID.help + @${TANGLE} -R"PrincipalIdealDomain.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PrincipalIdealDomain.input + @echo "PrincipalIdealDomain (PID)" >>${HELPFILE} + +${HELP}/PriorityQueueAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create PriorityQueueAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PriorityQueueAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PriorityQueueAggregate.help + @cp ${HELP}/PriorityQueueAggregate.help ${HELP}/PRQAGG.help + @${TANGLE} -R"PriorityQueueAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PriorityQueueAggregate.input + @echo "PriorityQueueAggregate (PRQAGG)" >>${HELPFILE} + ${HELP}/Product.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7935 create Product.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Product.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20271,6 +22458,18 @@ ${HELP}/Quaternion.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Quaternion.input @echo "Quaternion (QUAT)" >>${HELPFILE} +${HELP}/QuaternionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create QuaternionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"QuaternionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/QuaternionCategory.help + @cp ${HELP}/QuaternionCategory.help ${HELP}/QUATCAT.help + @${TANGLE} -R"QuaternionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/QuaternionCategory.input + @echo "QuaternionCategory (QUATCAT)" >>${HELPFILE} + ${HELP}/QuaternionCategoryFunctions2.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7949 create QuaternionCategoryFunctions2.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -20292,6 +22491,42 @@ ${HELP}/Queue.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Queue.input @echo "Queue (QUEUE)" >>${HELPFILE} +${HELP}/QueueAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create QueueAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"QueueAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/QueueAggregate.help + @cp ${HELP}/QueueAggregate.help ${HELP}/QUAGG.help + @${TANGLE} -R"QueueAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/QueueAggregate.input + @echo "QueueAggregate (QUAGG)" >>${HELPFILE} + +${HELP}/QuotientFieldCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create QuotientFieldCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"QuotientFieldCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/QuotientFieldCategory.help + @cp ${HELP}/QuotientFieldCategory.help ${HELP}/QFCAT.help + @${TANGLE} -R"QuotientFieldCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/QuotientFieldCategory.input + @echo "QuotientFieldCategory (QFCAT)" >>${HELPFILE} + +${HELP}/RadicalCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RadicalCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RadicalCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RadicalCategory.help + @cp ${HELP}/RadicalCategory.help ${HELP}/RADCAT.help + @${TANGLE} -R"RadicalCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RadicalCategory.input + @echo "RadicalCategory (RADCAT)" >>${HELPFILE} + ${HELP}/RadicalSolvePackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7955 create RadicalSolvePackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -20326,6 +22561,18 @@ ${HELP}/RationalFunctionSum.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/RationalFunctionSum.input @echo "RationalFunctionSum (SUMRF)" >>${HELPFILE} +${HELP}/RealClosedField.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RealClosedField.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RealClosedField.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RealClosedField.help + @cp ${HELP}/RealClosedField.help ${HELP}/RCFIELD.help + @${TANGLE} -R"RealClosedField.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RealClosedField.input + @echo "RealClosedField (RCFIELD)" >>${HELPFILE} + ${HELP}/RealClosure.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7970 create RealClosure.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"RealClosure.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20335,6 +22582,42 @@ ${HELP}/RealClosure.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/RealClosure.input @echo "RealClosure (RECLOS)" >>${HELPFILE} +${HELP}/RealConstant.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RealConstant.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RealConstant.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RealConstant.help + @cp ${HELP}/RealConstant.help ${HELP}/REAL.help + @${TANGLE} -R"RealConstant.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RealConstant.input + @echo "RealConstant (REAL)" >>${HELPFILE} + +${HELP}/RealNumberSystem.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RealNumberSystem.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RealNumberSystem.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RealNumberSystem.help + @cp ${HELP}/RealNumberSystem.help ${HELP}/RNS.help + @${TANGLE} -R"RealNumberSystem.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RealNumberSystem.input + @echo "RealNumberSystem (RNS)" >>${HELPFILE} + +${HELP}/RealRootCharacterizationCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RealRootCharacterizationCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RealRootCharacterizationCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RealRootCharacterizationCategory.help + @cp ${HELP}/RealRootCharacterizationCategory.help ${HELP}/RRCC.help + @${TANGLE} -R"RealRootCharacterizationCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RealRootCharacterizationCategory.input + @echo "RealRootCharacterizationCategory (RRCC)" >>${HELPFILE} + ${HELP}/RealSolvePackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7980 create RealSolvePackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -20345,6 +22628,42 @@ ${HELP}/RealSolvePackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/RealSolvePackage.input @echo "RealSolvePackage (REALSOLV)" >>${HELPFILE} +${HELP}/RectangularMatrixCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RectangularMatrixCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RectangularMatrixCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RectangularMatrixCategory.help + @cp ${HELP}/RectangularMatrixCategory.help ${HELP}/RMATCAT.help + @${TANGLE} -R"RectangularMatrixCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RectangularMatrixCategory.input + @echo "RectangularMatrixCategory (RMATCAT)" >>${HELPFILE} + +${HELP}/RecursivePolynomialCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RecursivePolynomialCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RecursivePolynomialCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RecursivePolynomialCategory.help + @cp ${HELP}/RecursivePolynomialCategory.help ${HELP}/RPOLCAT.help + @${TANGLE} -R"RecursivePolynomialCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RecursivePolynomialCategory.input + @echo "RecursivePolynomialCategory (RPOLCAT)" >>${HELPFILE} + +${HELP}/RecursiveAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RecursiveAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RecursiveAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RecursiveAggregate.help + @cp ${HELP}/RecursiveAggregate.help ${HELP}/RCAGG.help + @${TANGLE} -R"RecursiveAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RecursiveAggregate.input + @echo "RecursiveAggregate (RCAGG)" >>${HELPFILE} + ${HELP}/RegularTriangularSet.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7990 create RegularTriangularSet.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20357,6 +22676,66 @@ ${HELP}/RegularTriangularSet.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/RegularTriangularSet.input @echo "RegularTriangularSet (REGSET)" >>${HELPFILE} +${HELP}/RegularTriangularSetCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RegularTriangularSetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RegularTriangularSetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RegularTriangularSetCategory.help + @cp ${HELP}/RegularTriangularSetCategory.help ${HELP}/RSETCAT.help + @${TANGLE} -R"RegularTriangularSetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RegularTriangularSetCategory.input + @echo "RegularTriangularSetCategory (RSETCAT)" >>${HELPFILE} + +${HELP}/RetractableTo.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RetractableTo.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RetractableTo.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RetractableTo.help + @cp ${HELP}/RetractableTo.help ${HELP}/RETRACT.help + @${TANGLE} -R"RetractableTo.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RetractableTo.input + @echo "RetractableTo (RETRACT)" >>${HELPFILE} + +${HELP}/RightModule.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create RightModule.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"RightModule.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/RightModule.help + @cp ${HELP}/RightModule.help ${HELP}/RMODULE.help + @${TANGLE} -R"RightModule.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/RightModule.input + @echo "RightModule (RMODULE)" >>${HELPFILE} + +${HELP}/Ring.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Ring.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Ring.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Ring.help + @cp ${HELP}/Ring.help ${HELP}/RING.help + @${TANGLE} -R"Ring.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Ring.input + @echo "Ring (RING)" >>${HELPFILE} + +${HELP}/Rng.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create Rng.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"Rng.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/Rng.help + @cp ${HELP}/Rng.help ${HELP}/RNG.help + @${TANGLE} -R"Rng.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/Rng.input + @echo "Rng (RNG)" >>${HELPFILE} + ${HELP}/RomanNumeral.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8000 create RomanNumeral.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"RomanNumeral.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20396,6 +22775,42 @@ ${HELP}/SegmentBinding.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/SegmentBinding.input @echo "SegmentBinding (SEGBIND)" >>${HELPFILE} +${HELP}/SegmentCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SegmentCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SegmentCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SegmentCategory.help + @cp ${HELP}/SegmentCategory.help ${HELP}/SEGCAT.help + @${TANGLE} -R"SegmentCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SegmentCategory.input + @echo "SegmentCategory (SEGCAT)" >>${HELPFILE} + +${HELP}/SegmentExpansionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SegmentExpansionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SegmentExpansionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SegmentExpansionCategory.help + @cp ${HELP}/SegmentExpansionCategory.help ${HELP}/SEGXCAT.help + @${TANGLE} -R"SegmentExpansionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SegmentExpansionCategory.input + @echo "SegmentExpansionCategory (SEGXCAT)" >>${HELPFILE} + +${HELP}/SemiGroup.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SemiGroup.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SemiGroup.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SemiGroup.help + @cp ${HELP}/SemiGroup.help ${HELP}/SGROUP.help + @${TANGLE} -R"SemiGroup.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SemiGroup.input + @echo "SemiGroup (SGROUP)" >>${HELPFILE} + ${HELP}/Set.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8030 create Set.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Set.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20405,6 +22820,30 @@ ${HELP}/Set.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Set.input @echo "Set (SET)" >>${HELPFILE} +${HELP}/SetAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SetAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SetAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SetAggregate.help + @cp ${HELP}/SetAggregate.help ${HELP}/SETAGG.help + @${TANGLE} -R"SetAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SetAggregate.input + @echo "SetAggregate (SETAGG)" >>${HELPFILE} + +${HELP}/SetCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SetCategory.help + @cp ${HELP}/SetCategory.help ${HELP}/SETCAT.help + @${TANGLE} -R"SetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SetCategory.input + @echo "SetCategory (SETCAT)" >>${HELPFILE} + ${HELP}/SetCategoryWithDegree.help: ${BOOKS}/bookvol10.2.pamphlet @echo 8035 create SetCategoryWithDegree.help from \ ${BOOKS}/bookvol10.2.pamphlet @@ -20417,6 +22856,18 @@ ${HELP}/SetCategoryWithDegree.help: ${BOOKS}/bookvol10.2.pamphlet >${INPUT}/SetCategoryWithDegree.input @echo "SetCategoryWithDegree (SETCATD)" >>${HELPFILE} +${HELP}/SExpressionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SExpressionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SExpressionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SExpressionCategory.help + @cp ${HELP}/SExpressionCategory.help ${HELP}/SEXCAT.help + @${TANGLE} -R"SExpressionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SExpressionCategory.input + @echo "SExpressionCategory (SEXCAT)" >>${HELPFILE} + ${HELP}/SingleInteger.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8040 create SingleInteger.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"SingleInteger.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20447,6 +22898,18 @@ ${HELP}/SparseMultivariateTaylorSeries.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/SparseMultivariateTaylorSeries.input @echo "SparseMultivariateTaylorSeries (SMTS)" >>${HELPFILE} +${HELP}/SpecialFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SpecialFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SpecialFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SpecialFunctionCategory.help + @cp ${HELP}/SpecialFunctionCategory.help ${HELP}/SPFCAT.help + @${TANGLE} -R"SpecialFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SpecialFunctionCategory.input + @echo "SpecialFunctionCategory (SPFCAT)" >>${HELPFILE} + ${HELP}/SquareMatrix.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8070 create SquareMatrix.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"SquareMatrix.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20456,6 +22919,21 @@ ${HELP}/SquareMatrix.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/SquareMatrix.input @echo "SquareMatrix (SQMATRIX)" >>${HELPFILE} +${HELP}/SquareFreeNormalizedTriangularSetCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SquareFreeNormalizedTriangularSetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SquareFreeNormalizedTriangularSetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SquareFreeNormalizedTriangularSetCategory.help + @cp ${HELP}/SquareFreeNormalizedTriangularSetCategory.help \ + ${HELP}/SNTSCAT.help + @${TANGLE} -R"SquareFreeNormalizedTriangularSetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SquareFreeNormalizedTriangularSetCategory.input + @echo "SquareFreeNormalizedTriangularSetCategory (SNTSCAT)" \ + >>${HELPFILE} + ${HELP}/SquareFreeRegularTriangularSet.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8080 create SquareFreeRegularTriangularSet.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20468,6 +22946,32 @@ ${HELP}/SquareFreeRegularTriangularSet.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/SquareFreeRegularTriangularSet.input @echo "SquareFreeRegularTriangularSet (SREGSET)" >>${HELPFILE} +${HELP}/SquareFreeRegularTriangularSetCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SquareFreeRegularTriangularSetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SquareFreeRegularTriangularSetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SquareFreeRegularTriangularSetCategory.help + @cp ${HELP}/SquareFreeRegularTriangularSetCategory.help \ + ${HELP}/SFRTCAT.help + @${TANGLE} -R"SquareFreeRegularTriangularSetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SquareFreeRegularTriangularSetCategory.input + @echo "SquareFreeRegularTriangularSetCategory (SFRTCAT)" >>${HELPFILE} + +${HELP}/SquareMatrixCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create SquareMatrixCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"SquareMatrixCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/SquareMatrixCategory.help + @cp ${HELP}/SquareMatrixCategory.help ${HELP}/SMATCAT.help + @${TANGLE} -R"SquareMatrixCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/SquareMatrixCategory.input + @echo "SquareMatrixCategory (SMATCAT)" >>${HELPFILE} + ${HELP}/Stack.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8090 create Stack.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Stack.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20477,6 +22981,30 @@ ${HELP}/Stack.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Stack.input @echo "Stack (STACK)" >>${HELPFILE} +${HELP}/StackAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create StackAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"StackAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/StackAggregate.help + @cp ${HELP}/StackAggregate.help ${HELP}/SKAGG.help + @${TANGLE} -R"StackAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/StackAggregate.input + @echo "StackAggregate (SKAGG)" >>${HELPFILE} + +${HELP}/StepThrough.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create StepThrough.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"StepThrough.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/StepThrough.help + @cp ${HELP}/StepThrough.help ${HELP}/STEP.help + @${TANGLE} -R"StepThrough.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/StepThrough.input + @echo "StepThrough (STEP)" >>${HELPFILE} + ${HELP}/Stream.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8100 create Stream.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Stream.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20486,6 +23014,18 @@ ${HELP}/Stream.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Stream.input @echo "Stream (STREAM)" >>${HELPFILE} +${HELP}/StreamAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create StreamAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"StreamAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/StreamAggregate.help + @cp ${HELP}/StreamAggregate.help ${HELP}/STAGG.help + @${TANGLE} -R"StreamAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/StreamAggregate.input + @echo "StreamAggregate (STAGG)" >>${HELPFILE} + ${HELP}/String.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8110 create String.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"String.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20495,6 +23035,30 @@ ${HELP}/String.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/String.input @echo "String (STRING)" >>${HELPFILE} +${HELP}/StringAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create StringAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"StringAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/StringAggregate.help + @cp ${HELP}/StringAggregate.help ${HELP}/SRAGG.help + @${TANGLE} -R"StringAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/StringAggregate.input + @echo "StringAggregate (SRAGG)" >>${HELPFILE} + +${HELP}/StringCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create StringCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"StringCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/StringCategory.help + @cp ${HELP}/StringCategory.help ${HELP}/STRICAT.help + @${TANGLE} -R"StringCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/StringCategory.input + @echo "StringCategory (STRICAT)" >>${HELPFILE} + ${HELP}/StringTable.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8120 create StringTable.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"StringTable.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20522,6 +23086,18 @@ ${HELP}/Table.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Table.input @echo "Table (TABLE)" >>${HELPFILE} +${HELP}/TableAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create TableAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"TableAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/TableAggregate.help + @cp ${HELP}/TableAggregate.help ${HELP}/TBAGG.help + @${TANGLE} -R"TableAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/TableAggregate.input + @echo "TableAggregate (TBAGG)" >>${HELPFILE} + ${HELP}/TexFormat.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8145 create TexFormat.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"TexFormat.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20540,6 +23116,30 @@ ${HELP}/TextFile.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/TextFile.input @echo "TextFile (TEXTFILE)" >>${HELPFILE} +${HELP}/ThreeSpaceCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create ThreeSpaceCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"ThreeSpaceCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/ThreeSpaceCategory.help + @cp ${HELP}/ThreeSpaceCategory.help ${HELP}/SPACEC.help + @${TANGLE} -R"ThreeSpaceCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/ThreeSpaceCategory.input + @echo "ThreeSpaceCategory (SPACEC)" >>${HELPFILE} + +${HELP}/TranscendentalFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create TranscendentalFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"TranscendentalFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/TranscendentalFunctionCategory.help + @cp ${HELP}/TranscendentalFunctionCategory.help ${HELP}/TRANFUN.help + @${TANGLE} -R"TranscendentalFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/TranscendentalFunctionCategory.input + @echo "TranscendentalFunctionCategory (TRANFUN)" >>${HELPFILE} + ${HELP}/TransSolvePackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 8155 create TransSolvePackage.help from \ ${BOOKS}/bookvol10.4.pamphlet @@ -20550,6 +23150,30 @@ ${HELP}/TransSolvePackage.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/TransSolvePackage.input @echo "TransSolvePackage (SOLVETRA)" >>${HELPFILE} +${HELP}/TriangularSetCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create TriangularSetCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"TriangularSetCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/TriangularSetCategory.help + @cp ${HELP}/TriangularSetCategory.help ${HELP}/TSETCAT.help + @${TANGLE} -R"TriangularSetCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/TriangularSetCategory.input + @echo "TriangularSetCategory (TSETCAT)" >>${HELPFILE} + +${HELP}/TrigonometricFunctionCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create TrigonometricFunctionCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"TrigonometricFunctionCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/TrigonometricFunctionCategory.help + @cp ${HELP}/TrigonometricFunctionCategory.help ${HELP}/TRIGCAT.help + @${TANGLE} -R"TrigonometricFunctionCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/TrigonometricFunctionCategory.input + @echo "TrigonometricFunctionCategory (TRIGCAT)" >>${HELPFILE} + ${HELP}/TwoDimensionalArray.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8160 create TwoDimensionalArray.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20561,6 +23185,18 @@ ${HELP}/TwoDimensionalArray.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/TwoDimensionalArray.input @echo "TwoDimensionalArray (ARRAY2)" >>${HELPFILE} +${HELP}/TwoDimensionalArrayCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create TwoDimensionalArrayCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"TwoDimensionalArrayCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/TwoDimensionalArrayCategory.help + @cp ${HELP}/TwoDimensionalArrayCategory.help ${HELP}/ARR2CAT.help + @${TANGLE} -R"TwoDimensionalArrayCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/TwoDimensionalArrayCategory.input + @echo "TwoDimensionalArrayCategory (ARR2CAT)" >>${HELPFILE} + ${HELP}/TwoDimensionalViewport.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8170 create TwoDimensionalViewport.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20571,6 +23207,30 @@ ${HELP}/TwoDimensionalViewport.help: ${BOOKS}/bookvol10.3.pamphlet # Note:no input regression file due to graphics @echo "TwoDimensionalViewport (VIEW2D)" >>${HELPFILE} +${HELP}/UnaryRecursiveAggregate.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnaryRecursiveAggregate.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnaryRecursiveAggregate.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnaryRecursiveAggregate.help + @cp ${HELP}/UnaryRecursiveAggregate.help ${HELP}/URAGG.help + @${TANGLE} -R"UnaryRecursiveAggregate.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnaryRecursiveAggregate.input + @echo "UnaryRecursiveAggregate (URAGG)" >>${HELPFILE} + +${HELP}/UniqueFactorizationDomain.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UniqueFactorizationDomain.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UniqueFactorizationDomain.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UniqueFactorizationDomain.help + @cp ${HELP}/UniqueFactorizationDomain.help ${HELP}/UFD.help + @${TANGLE} -R"UniqueFactorizationDomain.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UniqueFactorizationDomain.input + @echo "UniqueFactorizationDomain (UFD)" >>${HELPFILE} + ${HELP}/UnivariatePolynomial.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8180 create UnivariatePolynomial.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20583,6 +23243,84 @@ ${HELP}/UnivariatePolynomial.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/UnivariatePolynomial.input @echo "UnivariatePolynomial (UP)" >>${HELPFILE} +${HELP}/UnivariateLaurentSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariateLaurentSeriesCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariateLaurentSeriesCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariateLaurentSeriesCategory.help + @cp ${HELP}/UnivariateLaurentSeriesCategory.help ${HELP}/ULSCAT.help + @${TANGLE} -R"UnivariateLaurentSeriesCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariateLaurentSeriesCategory.input + @echo "UnivariateLaurentSeriesCategory (ULSCAT)" >>${HELPFILE} + +${HELP}/UnivariateLaurentSeriesConstructorCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariateLaurentSeriesConstructorCategory.help \ + from ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariateLaurentSeriesConstructorCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariateLaurentSeriesConstructorCategory.help + @cp ${HELP}/UnivariateLaurentSeriesConstructorCategory.help \ + ${HELP}/ULSCCAT.help + @${TANGLE} -R"UnivariateLaurentSeriesConstructorCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariateLaurentSeriesConstructorCategory.input + @echo "UnivariateLaurentSeriesConstructorCategory (ULSCCAT)" \ + >>${HELPFILE} + +${HELP}/UnivariatePolynomialCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariatePolynomialCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariatePolynomialCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariatePolynomialCategory.help + @cp ${HELP}/UnivariatePolynomialCategory.help ${HELP}/UPOLYC.help + @${TANGLE} -R"UnivariatePolynomialCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariatePolynomialCategory.input + @echo "UnivariatePolynomialCategory (UPOLYC)" >>${HELPFILE} + +${HELP}/UnivariatePowerSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariatePowerSeriesCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariatePowerSeriesCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariatePowerSeriesCategory.help + @cp ${HELP}/UnivariatePowerSeriesCategory.help ${HELP}/UPSCAT.help + @${TANGLE} -R"UnivariatePowerSeriesCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariatePowerSeriesCategory.input + @echo "UnivariatePowerSeriesCategory (UPSCAT)" >>${HELPFILE} + +${HELP}/UnivariatePuiseuxSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariatePuiseuxSeriesCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariatePuiseuxSeriesCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariatePuiseuxSeriesCategory.help + @cp ${HELP}/UnivariatePuiseuxSeriesCategory.help ${HELP}/UPXSCAT.help + @${TANGLE} -R"UnivariatePuiseuxSeriesCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariatePuiseuxSeriesCategory.input + @echo "UnivariatePuiseuxSeriesCategory (UPXSCAT)" >>${HELPFILE} + +${HELP}/UnivariatePuiseuxSeriesConstructorCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariatePuiseuxSeriesConstructorCategory.help \ + from ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariatePuiseuxSeriesConstructorCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariatePuiseuxSeriesConstructorCategory.help + @cp ${HELP}/UnivariatePuiseuxSeriesConstructorCategory.help \ + ${HELP}/UPXSCCA.help + @${TANGLE} -R"UnivariatePuiseuxSeriesConstructorCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariatePuiseuxSeriesConstructorCategory.input + @echo "UnivariatePuiseuxSeriesConstructorCategory (UPXSCCA)" \ + >>${HELPFILE} + ${HELP}/UnivariateSkewPolynomial.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8190 create UnivariateSkewPolynomial.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20595,6 +23333,18 @@ ${HELP}/UnivariateSkewPolynomial.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/UnivariateSkewPolynomial.input @echo "UnivariateSkewPolynomial (OREUP)" >>${HELPFILE} +${HELP}/UnivariateSkewPolynomialCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariateSkewPolynomialCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariateSkewPolynomialCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariateSkewPolynomialCategory.help + @cp ${HELP}/UnivariateSkewPolynomialCategory.help ${HELP}/OREPCAT.help + @${TANGLE} -R"UnivariateSkewPolynomialCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariateSkewPolynomialCategory.input + @echo "UnivariateSkewPolynomialCategory (OREPCAT)" >>${HELPFILE} + ${HELP}/UnivariateTaylorSeriesCZero.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8195 create UnivariateTaylorSeriesCZero.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20607,6 +23357,18 @@ ${HELP}/UnivariateTaylorSeriesCZero.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/UnivariateTaylorSeriesCZero.input @echo "UnivariateTaylorSeriesCZero (UTSZ)" >>${HELPFILE} +${HELP}/UnivariateTaylorSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create UnivariateTaylorSeriesCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"UnivariateTaylorSeriesCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/UnivariateTaylorSeriesCategory.help + @cp ${HELP}/UnivariateTaylorSeriesCategory.help ${HELP}/UTSCAT.help + @${TANGLE} -R"UnivariateTaylorSeriesCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/UnivariateTaylorSeriesCategory.input + @echo "UnivariateTaylorSeriesCategory (UTSCAT)" >>${HELPFILE} + ${HELP}/UniversalSegment.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8200 create UniversalSegment.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20626,6 +23388,30 @@ ${HELP}/Vector.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Vector.input @echo "Vector (VECTOR)" >>${HELPFILE} +${HELP}/VectorCategory.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create VectorCategory.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"VectorCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/VectorCategory.help + @cp ${HELP}/VectorCategory.help ${HELP}/VECTCAT.help + @${TANGLE} -R"VectorCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/VectorCategory.input + @echo "VectorCategory (VECTCAT)" >>${HELPFILE} + +${HELP}/VectorSpace.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create VectorSpace.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"VectorSpace.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/VectorSpace.help + @cp ${HELP}/VectorSpace.help ${HELP}/VSPACE.help + @${TANGLE} -R"VectorSpace.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/VectorSpace.input + @echo "VectorSpace (VSPACE)" >>${HELPFILE} + ${HELP}/Void.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8220 create Void.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Void.help" ${BOOKS}/bookvol10.3.pamphlet \ @@ -20647,6 +23433,30 @@ ${HELP}/WuWenTsunTriangularSet.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/WuWenTsunTriangularSet.input @echo "WuWenTsunTriangularSet (WUTSET)" >>${HELPFILE} +${HELP}/XAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create XAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"XAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/XAlgebra.help + @cp ${HELP}/XAlgebra.help ${HELP}/XALG.help + @${TANGLE} -R"XAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/XAlgebra.input + @echo "XAlgebra (XALG)" >>${HELPFILE} + +${HELP}/XFreeAlgebra.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create XFreeAlgebra.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"XFreeAlgebra.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/XFreeAlgebra.help + @cp ${HELP}/XFreeAlgebra.help ${HELP}/XFALG.help + @${TANGLE} -R"XFreeAlgebra.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/XFreeAlgebra.input + @echo "XFreeAlgebra (XFALG)" >>${HELPFILE} + ${HELP}/XPBWPolynomial.help: ${BOOKS}/bookvol10.3.pamphlet @echo 8240 create XPBWPolynomial.help from \ ${BOOKS}/bookvol10.3.pamphlet @@ -20683,6 +23493,18 @@ ${HELP}/XPolynomialRing.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/XPolynomialRing.input @echo "XPolynomialRing (XPR)" >>${HELPFILE} +${HELP}/XPolynomialsCat.help: ${BOOKS}/bookvol10.2.pamphlet + @echo 5000 create XPolynomialsCat.help from \ + ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"XPolynomialsCat.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/XPolynomialsCat.help + @cp ${HELP}/XPolynomialsCat.help ${HELP}/XPOLYC.help + @${TANGLE} -R"XPolynomialsCat.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/XPolynomialsCat.input + @echo "XPolynomialsCat (XPOLYC)" >>${HELPFILE} + ${HELP}/ZeroDimensionalSolvePackage.help: ${BOOKS}/bookvol10.4.pamphlet @echo 8270 create ZeroDimensionalSolvePackage.help from \ ${BOOKS}/bookvol10.4.pamphlet diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 1c35684..6034fff 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2828,5 +2828,7 @@ May 2010 release src/axiom-website/download.html add new binaries
20100529.03.tpd.patch books/bookvolbib AL94 Adams, William W. and Loustaunau, Philippe
+20100529.04.tpd.patch +books/bookvol10.2 add test and help files for all categories