diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet index 606738e..281747b 100644 --- a/books/bookvol10.2.pamphlet +++ b/books/bookvol10.2.pamphlet @@ -48068,6 +48068,349 @@ digraph pic { @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{PseudoAlgebraicClosureOfPerfectFieldCategory}{PACPERC} +\pagepic{ps/v102PseudoAlgebraicClosureOfPerfectFieldCategory.ps}{PACPERC}{0.50} +<>= +)set break resume +)sys rm -f PseudoAlgebraicClosureOfPerfectFieldCategory.output +)spool PseudoAlgebraicClosureOfPerfectFieldCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PseudoAlgebraicClosureOfPerfectFieldCategory +--R PseudoAlgebraicClosureOfPerfectFieldCategory is a category constructor +--R Abbreviation for PseudoAlgebraicClosureOfPerfectFieldCategory is PACPERC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PACPERC +--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 conjugate : % -> % +--R definingPolynomial : % -> SUP % definingPolynomial : () -> SUP % +--R extDegree : % -> PI factor : % -> Factored % +--R fullOutput : % -> OutputForm gcd : List % -> % +--R gcd : (%,%) -> % ground? : % -> Boolean +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % lift : (%,%) -> SUP % +--R lift : % -> SUP % maxTower : List % -> % +--R newElement : (SUP %,Symbol) -> % one? : % -> Boolean +--R previousTower : % -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reduce : SUP % -> % ?rem? : (%,%) -> % +--R sample : () -> % setTower! : % -> Void +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % vectorise : (%,%) -> Vector % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List % +--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 newElement : (SUP %,%,Symbol) -> % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PseudoAlgebraicClosureOfPerfectFieldCategory examples +==================================================================== + +See Also: +o )show PseudoAlgebraicClosureOfPerfectFieldCategory + +@ + +\pagefrom{DivisionRing}{DIVRING} +\pagefrom{Field}{FIELD} +\pagefrom{EuclideanDomain}{EUCDOM} +\pagefrom{UniqueFactorizationDomain}{UFD} + +{\bf Exports:} +\begin{tabular}{llll} +\cross{PACPERC}{0} & +\cross{PACPERC}{1} & +\cross{PACPERC}{associates?} & +\cross{PACPERC}{characteristic} \\ +\cross{PACPERC}{coerce} & +\cross{PACPERC}{conjugate} & +\cross{PACPERC}{definingPolynomial} & +\cross{PACPERC}{distinguishedRootsOf} \\ +\cross{PACPERC}{divide} & +\cross{PACPERC}{euclideanSize} & +\cross{PACPERC}{expressIdealMember} & +\cross{PACPERC}{exquo} \\ +\cross{PACPERC}{extDegree} & +\cross{PACPERC}{extendedEuclidean} & +\cross{PACPERC}{factor} & +\cross{PACPERC}{fullOutput} \\ +\cross{PACPERC}{gcd} & +\cross{PACPERC}{gcdPolynomial} & +\cross{PACPERC}{ground?} & +\cross{PACPERC}{hash} \\ +\cross{PACPERC}{inv} & +\cross{PACPERC}{latex} & +\cross{PACPERC}{lcm} & +\cross{PACPERC}{lift} \\ +\cross{PACPERC}{maxTower} & +\cross{PACPERC}{multiEuclidean} & +\cross{PACPERC}{newElement} & +\cross{PACPERC}{one?} \\ +\cross{PACPERC}{previousTower} & +\cross{PACPERC}{prime?} & +\cross{PACPERC}{principalIdeal} & +\cross{PACPERC}{?quo?} \\ +\cross{PACPERC}{recip} & +\cross{PACPERC}{reduce} & +\cross{PACPERC}{?rem?} & +\cross{PACPERC}{sample} \\ +\cross{PACPERC}{setTower!} & +\cross{PACPERC}{sizeLess?} & +\cross{PACPERC}{squareFree} & +\cross{PACPERC}{squareFreePart} \\ +\cross{PACPERC}{subtractIfCan} & +\cross{PACPERC}{unit?} & +\cross{PACPERC}{unitCanonical} & +\cross{PACPERC}{unitNormal} \\ +\cross{PACPERC}{vectorise} & +\cross{PACPERC}{zero?} & +\cross{PACPERC}{?*?} & +\cross{PACPERC}{?**?} \\ +\cross{PACPERC}{?+?} & +\cross{PACPERC}{?-?} & +\cross{PACPERC}{-?} & +\cross{PACPERC}{?/?} \\ +\cross{PACPERC}{?=?} & +\cross{PACPERC}{?\^{}?} & +\cross{PACPERC}{?\~{}=?} & +\end{tabular} + +{\bf Attributes Exported:} +\begin{itemize} +\item {\bf \cross{PACPERC}{canonicalUnitNormal}} +is true if we can choose a canonical representative for each class +of associate elements, that is {\tt associates?(a,b)} returns true +if and only if {\tt unitCanonical(a) = unitCanonical(b)}. +\item {\bf \cross{PACPERC}{canonicalsClosed}} +is true if\hfill\\ +{\tt unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}. +\item {\bf \cross{PACPERC}{noZeroDivisors}} +is true if $x * y \ne 0$ implies both x and y are non-zero. +\item {\bf \cross{PACPERC}{commutative(``*'')}} +is true if it has an operation $"*": (D,D) -> D$ +which is commutative. +\item {\bf \cross{PACPERC}{unitsKnown}} +is true if a monoid (a multiplicative semigroup with a 1) has +unitsKnown means that the operation {\tt recip} can only return +``failed'' if its argument is not a unit. +\item {\bf \cross{PACPERC}{leftUnitary}} +is true if $1 * x = x$ for all x. +\item {\bf \cross{PACPERC}{rightUnitary}} +is true if $x * 1 = x$ for all x. +\end{itemize} + +These are directly exported but not implemented: +\begin{verbatim} + conjugate: % -> % + definingPolynomial: () -> SUP(%) + definingPolynomial: % -> SUP % + distinguishedRootsOf: (SparseUnivariatePolynomial %,%) -> List % + extDegree: % -> PI + fullOutput: % -> OutputForm + ground_? : % -> Boolean + lift: % -> SUP(%) + lift: (%,%) -> SUP(%) + maxTower: List % -> % + newElement: (SUP(%), %, Symbol) -> % + newElement: (SUP(%), Symbol) -> % + previousTower: % -> % + reduce: SUP(%) -> % + setTower_!: % -> Void + vectorise: (%,%) -> Vector(%) +\end{verbatim} + +These exports come from \refto{Field}(): +\begin{verbatim} + associates? : (%,%) -> Boolean + divide : (%,%) -> Record(quotient: %,remainder: %) + euclideanSize : % -> NonNegativeInteger + exquo : (%,%) -> Union(%,"failed") + factor : % -> Factored % + gcd : (%,%) -> % + inv : % -> % + prime? : % -> Boolean + squareFree : % -> Factored % + unitCanonical : % -> % + unitNormal : % -> Record(unit: %,canonical: %,associate: %) + ?/? : (%,%) -> % +\end{verbatim} + +These exports come from \refto{EuclideanDomain}(): +\begin{verbatim} + 0 : () -> % + 1 : () -> % + characteristic : () -> NonNegativeInteger + coerce : % -> % + coerce : Integer -> % + coerce : % -> OutputForm + expressIdealMember : (List %,%) -> Union(List %,"failed") + extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") + extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) + gcd : List % -> % + gcdPolynomial : (SparseUnivariatePolynomial %, + SparseUnivariatePolynomial %) -> + SparseUnivariatePolynomial % + hash : % -> SingleInteger + latex : % -> String + lcm : List % -> % + lcm : (%,%) -> % + multiEuclidean : (List %,%) -> Union(List %,"failed") + one? : % -> Boolean + principalIdeal : List % -> Record(coef: List %,generator: %) + recip : % -> Union(%,"failed") + sample : () -> % + sizeLess? : (%,%) -> Boolean + subtractIfCan : (%,%) -> Union(%,"failed") + unit? : % -> Boolean + zero? : % -> Boolean + ?+? : (%,%) -> % + ?=? : (%,%) -> Boolean + ?~=? : (%,%) -> Boolean + ?*? : (%,%) -> % + ?*? : (Integer,%) -> % + ?*? : (PositiveInteger,%) -> % + ?*? : (NonNegativeInteger,%) -> % + ?-? : (%,%) -> % + -? : % -> % + ?**? : (%,PositiveInteger) -> % + ?**? : (%,NonNegativeInteger) -> % + ?^? : (%,PositiveInteger) -> % + ?^? : (%,NonNegativeInteger) -> % + ?quo? : (%,%) -> % + ?rem? : (%,%) -> % +\end{verbatim} + +These exports come from \refto{UniqueFactorizationDomain}(): +\begin{verbatim} + squareFreePart : % -> % +\end{verbatim} + + +These exports come from \refto{DivisionRing}(): +\begin{verbatim} + coerce : Fraction Integer -> % + ?*? : (Fraction Integer,%) -> % + ?*? : (%,Fraction Integer) -> % + ?**? : (%,Integer) -> % + ?^? : (%,Integer) -> % +\end{verbatim} + +<>= +)abbrev category PACPERC PseudoAlgebraicClosureOfPerfectFieldCategory +++ Authors: Gaetan Hache +++ Date Created: may 1997 +++ Date Last Updated: April 2010, by Tim Daly +++ Description: This category exports the function for domains +++ which implement dynamic extension using the simple notion of tower +++ extensions. ++ A tower extension T of the ground +++ field K is any sequence of field extension +++ (T : K_0, K_1, ..., K_i...,K_n) where K_0 = K +++ and for i =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 +++ and defined by an irreducible polynomial p(Z) in K_{i-1}. +++ Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) +++ and (T_2: K_02, K_12,...,K_i2,...,K_n2) +++ are said to be related if T_1 <= T_2 (or T_1 >= T_2), +++ that is if K_i1 = K_i2 for i=1,2,...,n1 (or i=1,2,...,n2). +++ Any algebraic operations defined for several elements +++ are only defined if all of the concerned elements are comming from +++ a set of related tour extensions. +PseudoAlgebraicClosureOfPerfectFieldCategory : Category == Field with + + definingPolynomial: () -> SUP(%) + definingPolynomial: % -> SUP % + + lift: % -> SUP(%) + lift: (%,%) -> SUP(%) + reduce: SUP(%) -> % + + distinguishedRootsOf: (SparseUnivariatePolynomial %,%) -> List % + ++ distinguishedRootsOf(p,a) returns a (distinguised) root for each + ++ irreducible factor of the polynomial p (factored over the field defined + ++ by the element a). + + ground_? : % -> Boolean + maxTower: List % -> % + ++ maxTower(l) returns the tower in the list having the maximal extension + ++ degree over the ground field. It has no meaning if the towers are + ++ not related. + extDegree: % -> PI + ++ extDegree(a) returns the extension degree of the extension tower + ++ over which the element is defined. + previousTower: % -> % + ++ previousTower(a) returns the previous tower extension over which + ++ the element a is defined. + + vectorise: (%,%) -> Vector(%) + + conjugate: % -> % + newElement: (SUP(%), %, Symbol) -> % + newElement: (SUP(%), Symbol) -> % + setTower_!: % -> Void + fullOutput: % -> OutputForm + +@ +<>= +"PACPERC" [color=lightblue,href="bookvol10.2.pdf#nameddest=PACPERC"]; +"PACPERC" -> "FIELD" + +@ +<>= +"PseudoAlgebraicClosureOfPerfectFieldCategory" + [color=lightblue,href="bookvol10.2.pdf#nameddest=PACPERC"]; +"PseudoAlgebraicClosureOfPerfectFieldCategory" -> "Field()" + +@ +<>= +digraph pic { + fontsize=10; + bgcolor="#FFFF66"; + node [shape=box, color=white, style=filled]; + +"PseudoAlgebraicClosureOfPerfectFieldCategory" [color=lightblue]; +"PseudoAlgebraicClosureOfPerfectFieldCategory" -> "FIELD..." + +"FIELD..." [color=lightblue]; + +} + +@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{QuotientFieldCategory}{QFCAT} \pagepic{ps/v102quotientfieldcategory.ps}{QFCAT}{0.50} diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index d72e7b9..b86d067 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -24469,6 +24469,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|PrimitiveFunctionCategory| . PRIMCAT) (|PrincipalIdealDomain| . PID) (|PriorityQueueAggregate| . PRQAGG) + (|PseudoAlgebraicClosureOfPerfectFieldCategory| . PACPERC) (|QuaternionCategory| . QUATCAT) (|QueueAggregate| . QUAGG) (|QuotientFieldCategory| . 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moveto +134 36 lineto +134 0 lineto +204 0 lineto +closepath stroke +0.000 0.000 0.000 nodecolor +14 /Times-Roman set_font +141.5 13.9 moveto 55 (FIELD...) alignedtext +grestore +% PseudoAlgebraicClosureOfPerfectFieldCategory->FIELD... +gsave +1 setlinewidth +0.000 0.000 0.000 edgecolor +newpath 169 72 moveto +169 64 169 55 169 46 curveto +stroke +0.000 0.000 0.000 edgecolor +newpath 172.5 46 moveto +169 36 lineto +165.5 46 lineto +closepath fill +1 setlinewidth +solid +0.000 0.000 0.000 edgecolor +newpath 172.5 46 moveto +169 36 lineto +165.5 46 lineto +closepath stroke +grestore +endpage +showpage +grestore +%%PageTrailer +%%EndPage: 1 +%%Trailer +%%Pages: 1 +%%BoundingBox: 36 36 382 152 +end +restore +%%EOF diff --git a/changelog b/changelog index d354f1b..0e5772f 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,8 @@ +20100423 tpd src/axiom-website/patches.html 20100423.01.tpd.patch +20100423 tpd src/algebra/Makefile add PACPERC help and regression +20100423 tpd books/bookvol5 add PseudoAlgebraicClosureOfPerfectFieldCategory +20100423 tpd books/ps/v102PseudoAlgebraicClosureOfPerfectFieldCategory.ps added +20100423 tpd books/bookvol10.2 add PseudoAlgebraicClosureOfPerfectFieldCategory 20100422 tpd src/axiom-website/patches.html 20100422.03.tpd.patch 20100422 tpd books/bookvol4 document process to add new algebra 20100422 tpd src/axiom-website/patches.html 20100422.02.tpd.patch diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index fb8be9b..a228636 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -1813,7 +1813,7 @@ LAYER6=\ /*"FAMONOID" -> {"OCAMON"; "OAMON"; "OASGP"; "ORDSET"; "NNI"; "INT"}*/ /*"FAMONOID" -> {"MONOID"; "SGROUP"}*/ -"FIELD" [color="#4488FF",href="bookvol10.2.pdf#nameddest=FIELD"] +"FIELD" [color="#4488FF",href="bookvol10.2.pdf#nameddest=FIELD"] /*"FIELD" -> "EUCDOM"*/ "FIELD" -> "PID" /*"FIELD" -> {"GCDDOM"; "INTDOM"; "COMRING"; "RING"; "RNG"; "ABELGRP"}*/ @@ -2234,6 +2234,7 @@ LAYER7=\ ${OUT}/MRING.o ${OUT}/MTHING.o ${OUT}/NCNTFRAC.o ${OUT}/NCODIV.o \ ${OUT}/NUMTUBE.o ${OUT}/ODR.o ${OUT}/OFMONOID.o ${OUT}/ONECOMP.o \ ${OUT}/ORDCOMP.o ${OUT}/OREPCAT.o ${OUT}/OREPCAT-.o ${OUT}/OWP.o \ + ${OUT}/PACPERC.o \ ${OUT}/PADIC.o ${OUT}/PATTERN2.o ${OUT}/PATLRES.o ${OUT}/PARTPERM.o \ ${OUT}/PBWLB.o ${OUT}/PENDTREE.o ${OUT}/PGE.o ${OUT}/PGROEB.o \ ${OUT}/PINTERP.o ${OUT}/PLOTTOOL.o ${OUT}/PFR.o ${OUT}/PMDOWN.o \ @@ -3112,6 +3113,14 @@ LAYER7=\ "OWP" -> "FIELD" /*"OWP" -> {"EUCDOM"; "PID"; "GCDDOM"; "INTDOM"; "ENTIRER"; "UFD"; "DIVRING"}*/ +"PACPERC" [color="#88FF44",href="bookvol10.2.pdf#nameddest=PACPERC"] +"PACPERC" -> "FIELD" +/*"PACPERC" -> {"EUCDOM"; "PID"; "GCDDOM"; "INTDOM"; "COMRING"}*/ +/*"PACPERC" -> {"RING"; "RNG"; "ABELGRP"; "CABMON"; "ABELMON"}*/ +/*"PACPERC" -> {"ABELSG"; "SETCAT"; "BASTYPE"; "KOERCE"}*/ +/*"PACPERC" -> {"SGROUP"; "MONOID"; "LMODULE"; "BMODULE" }*/ +/*"PACPERC" -> {"RMODULE"; "ALGEBRA"; "MODULE"; "ENTIRER"; "UFD"; "DIVRING"}*/ + "PADIC" [color="#88FF44",href="bookvol10.3.pdf#nameddest=PADIC"] /*"PADIC" -> "BOOLEAN"*/ "PADIC" -> "PADICCT" @@ -16633,6 +16642,7 @@ SPADHELP=\ ${HELP}/Permutation.help \ ${HELP}/Polynomial.help \ ${HELP}/Product.help \ + ${HELP}/PseudoAlgebraicClosureOfPerfectFieldCategory.help \ ${HELP}/Quaternion.help \ ${HELP}/QuaternionCategoryFunctions2.help \ ${HELP}/Queue.help \ @@ -16775,8 +16785,9 @@ REGRESS= \ Permutation.regress \ PlaneAlgebraicCurvePlot.regress \ Plot.regress \ - Product.regress \ Polynomial.regress \ + Product.regress \ + PseudoAlgebraicClosureOfPerfectFieldCategory.regress \ Quaternion.regress \ QuaternionCategoryFunctions2.regress \ Queue.regress \ @@ -17918,6 +17929,21 @@ ${HELP}/Product.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Product.input @echo "Product (PRODUCT)" >>${HELPFILE} +${HELP}/PseudoAlgebraicClosureOfPerfectFieldCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 7937 create PseudoAlgebraicClosureOfPerfectFieldCategory.help \ + from ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PseudoAlgebraicClosureOfPerfectFieldCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PseudoAlgebraicClosureOfPerfectFieldCategory.help + @cp ${HELP}/PseudoAlgebraicClosureOfPerfectFieldCategory.help \ + ${HELP}/PACPERC.help + @${TANGLE} -R"PseudoAlgebraicClosureOfPerfectFieldCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PseudoAlgebraicClosureOfPerfectFieldCategory.input + @echo "PseudoAlgebraicClosureOfPerfectFieldCategory (PACPERC)" \ + >>${HELPFILE} + ${HELP}/Quaternion.help: ${BOOKS}/bookvol10.3.pamphlet @echo 7940 create Quaternion.help from ${BOOKS}/bookvol10.3.pamphlet @${TANGLE} -R"Quaternion.help" ${BOOKS}/bookvol10.3.pamphlet \ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 45058d5..0cd51fb 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2657,5 +2657,7 @@ books/bookvol10.4 add InterfaceGroebnerPackage
books/bookvol10.5 fix missing INTERGB package
20100422.03.tpd.patch books/bookvol4 document process to add new algebra
+20100423.01.tpd.patch +books/bookvol10.2 add PseudoAlgebraicClosureOfPerfectFieldCategory