diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet index 42c5029..3ef9743 100644 --- a/books/bookvol10.4.pamphlet +++ b/books/bookvol10.4.pamphlet @@ -24919,6 +24919,285 @@ FiniteDivisorFunctions2(R1, UP1, UPUP1, F1, R2, UP2, UPUP2, F2): "FDIV2" -> "FFCAT" @ + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect} +<>= +)set break resume +)sys rm -f FiniteFieldFactorizationWithSizeParseBySideEffect.output +)spool FiniteFieldFactorizationWithSizeParseBySideEffect.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldFactorizationWithSizeParseBySideEffect +--R FiniteFieldFactorizationWithSizeParseBySideEffect(K: FiniteFieldCategory,PolK: UnivariatePolynomialCategory K) is a package constructor +--R Abbreviation for FiniteFieldFactorizationWithSizeParseBySideEffect is FFFACTSE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFFACTSE +--R +--R------------------------------- Operations -------------------------------- +--R factor : PolK -> Factored PolK irreducible? : PolK -> Boolean +--R factorCantorZassenhaus : (PolK,NonNegativeInteger) -> List PolK +--R factorSquareFree : PolK -> List PolK +--R factorUsingMusser : PolK -> Factored PolK +--R factorUsingYun : PolK -> Factored PolK +--R +--E 1 + +)spool +)lisp (bye) +@ + +<>= +==================================================================== +FiniteFieldFactorizationWithSizeParseBySideEffect examples +==================================================================== + +See Also: +o )show FiniteFieldFactorizationWithSizeParseBySideEffect + +@ +\pagehead{FiniteFieldFactorizationWithSizeParseBySideEffect}{FFFACTSE} +\pagepic{ps/v104finitefieldfactorizationwithsizeparsebysideeffect.ps}{FFFACTSE}{1.00} + +{\bf Exports:}\\ +\begin{tabular}{lll} +\cross{FFFACTSE}{factor} & +\cross{FFFACTSE}{factorCantorZassenhaus} & +\cross{FFFACTSE}{factorSquareFree} \\ +\cross{FFFACTSE}{factorUsingMusser} & +\cross{FFFACTSE}{factorUsingYun} & +\cross{FFFACTSE}{irreducible?} +\end{tabular} + + +<>= +)abbrev package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect +++ Author: Patrice Naudin, Claude Quitte, Kaj Laursen +++ Date Created: September 1996 +++ Date Last Updated: April 2010 by Tim Daly +++ Description: +++ Part of the package for Algebraic Function Fields in one variable (PAFF) +++ It has been modified (very slitely) so that each time the "factor" +++ function is used, the variable related to the size of the field +++ over which the polynomial is factorized is reset. This is done in +++ order to be used with a "dynamic extension field" which size is not +++ fixed but set before calling the "factor" function and which is +++ parse by side effect to this package via the function "size". See +++ the local function "initialize" of this package. +FiniteFieldFactorizationWithSizeParseBySideEffect(K : FiniteFieldCategory, + PolK : UnivariatePolynomialCategory(K)) : with + + factorSquareFree : PolK -> List(PolK) + factorCantorZassenhaus : (PolK, NonNegativeInteger) -> List(PolK) + factor : PolK -> Factored(PolK) + factorUsingYun : PolK -> Factored(PolK) + factorUsingMusser : PolK -> Factored(PolK) + irreducible? : PolK -> Boolean + + == add + + import FiniteFieldSquareFreeDecomposition(K, PolK) + p : NonNegativeInteger := characteristic()$K + p' : NonNegativeInteger := p quo 2 -- used for odd p : (p-1)/2 + q : NonNegativeInteger := size()$K + q' : NonNegativeInteger := q quo 2 -- used for odd q : (q-1)/2 + X : PolK := monomial(1, 1) + primeKdim : NonNegativeInteger := + q_quo_p : NonNegativeInteger := q quo p ; e : NonNegativeInteger := 1 + while q_quo_p > 1 repeat (e := e + 1 ; q_quo_p := q_quo_p quo p) + e + + initialize(): Void() == + q : NonNegativeInteger := size()$K + q' : NonNegativeInteger := q quo 2 -- used for odd q : (q-1)/2 + primeKdim : NonNegativeInteger := + q_quo_p : NonNegativeInteger := q quo p ; e:NonNegativeInteger := 1 + while q_quo_p > 1 repeat (e := e + 1 ; q_quo_p := q_quo_p quo p) + e + + exp(P : PolK, n : NonNegativeInteger, R : PolK) : PolK == + PP : PolK := P rem R ; Q : PolK := 1 + repeat + if odd?(n) then Q := Q * PP rem R + (n := n quo 2) = 0 => leave + PP := PP * PP rem R + return Q + + pPowers(P : PolK) : PrimitiveArray(PolK) == -- P is monic + n := degree(P) + result : PrimitiveArray(PolK) := new(n, 1) + result(1) := Qi := Q := exp(X, p, P) + for i in 2 .. n-1 repeat (Qi := Qi*Q rem P ; result(i) := Qi) + return result + + pExp(Q : PolK, Xpowers : PrimitiveArray(PolK)) : PolK == + Q' : PolK := 0 + while Q ^= 0 repeat + Q':=Q' +primeFrobenius(leadingCoefficient(Q)) * Xpowers(degree(Q)) + Q := reductum(Q) + return Q' + + pTrace(Q : PolK, d : NonNegativeInteger, P : PolK, + Xpowers : PrimitiveArray(PolK)) : PolK == + Q : PolK := Q rem P + result : PolK := Q + for i in 1 .. d-1 repeat result := Q + pExp(result, Xpowers) + return result rem P + + random(n : NonNegativeInteger) : PolK == + repeat + if (deg := (random(n)$Integer)::NonNegativeInteger) > 0 then leave + repeat + if (x : K := random()$K) ^= 0 then leave + result : PolK := + monomial(x, deg) + +/[monomial(random()$K, i) for i in 0 .. deg-1] + return result + + internalFactorCZ(P : PolK, -- P monic-squarefree + d:NonNegativeInteger, Xpowers:PrimitiveArray(PolK)) : List(PolK) == + + listOfFactors : List(PolK) := [P] + degree(P) = d => return listOfFactors + result : List(PolK) := [] + pDim : NonNegativeInteger := d * primeKdim + Q : PolK := P + + repeat + G := pTrace(random(degree(Q)), pDim, Q, Xpowers) + if p > 2 then G := exp(G, p', Q) - 1 + Q1 := gcd(G, Q) ; d1 := degree(Q1) + if d1 > 0 and d1 < degree(Q) then + listOfFactors := rest(listOfFactors) + if d1 = d then result := cons(Q1, result) + else listOfFactors := cons(Q1, listOfFactors) + Q1 := Q quo Q1 ; d1 := degree(Q1) + if d1 = d then result := cons(Q1, result) + else listOfFactors := cons(Q1, listOfFactors) + if empty?(listOfFactors) then leave + Q := first(listOfFactors) + return result + + internalFactorSquareFree(P:PolK):List(PolK) == -- P is monic-squareFree + degree(P) = 1 => [P] + result : List(PolK) := [] + Xpowers : PrimitiveArray(PolK) := pPowers(P) + S : PolK := Xpowers(1) + for j in 1..primeKdim-1 repeat S := pExp(S, Xpowers) + for i in 1 .. repeat -- S = X**(q**i) mod P + if degree(R := gcd(S - X, P)) > 0 then + result := concat(internalFactorCZ(R, i, Xpowers), result) + if degree (P) = degree (R) then return result + P := P quo R + if i >= degree(P) quo 2 then return cons(P, result) + for j in 0 .. degree(P)-1 repeat Xpowers(j):=Xpowers(j) rem P + S := S rem P + else if i >= degree(P) quo 2 then return cons(P, result) + for j in 1 .. primeKdim repeat S := pExp(S, Xpowers) + + internalFactor(P:PolK, sqrfree:PolK -> Factored(PolK)) : Factored(PolK) == + result : Factored(PolK) + if (d := minimumDegree(P)) > 0 then + P := P quo monomial(1, d) + result := primeFactor(X, d) + else + result := 1 + degree(P) = 0 => P * result + if (lcP := leadingCoefficient(P)) ^= 1 then P := inv(lcP) * P + degree(P) = 1 => lcP::PolK * primeFactor(P, 1) * result + sqfP : Factored(PolK) := sqrfree(P) + for x in factors(sqfP) repeat + xFactors : List(PolK) := internalFactorSquareFree(x.factor) + result:=result * */[primeFactor(Q, x.exponent) for Q in xFactors] + return lcP::PolK * result + + factorUsingYun(P : PolK) : Factored(PolK) == internalFactor(P, Yun) + + factorUsingMusser(P : PolK) : Factored(PolK) == internalFactor(P, Musser) + + factor(P : PolK) : Factored(PolK) == + initialize() + factorUsingYun(P) + + factorSquareFree(P : PolK) : List(PolK) == + degree(P) = 0 => [] + discriminant(P) = 0 => error("factorSquareFree : non quadratfrei") + if (lcP := leadingCoefficient(P)) ^= 1 then P := inv(lcP) * P + return internalFactorSquareFree(P) + + factorCantorZassenhaus(P : PolK, d : NonNegativeInteger) : List(PolK) == + if (lcP := leadingCoefficient(P)) ^= 1 then P := inv(lcP) * P + degree(P) = 1 => [P] + return internalFactorCZ(P, d, pPowers(P)) + + qExp(Q : PolK, XqPowers : PrimitiveArray(PolK)) : PolK == + Q' : PolK := 0 + while Q ^= 0 repeat + Q' := Q' + leadingCoefficient(Q) * XqPowers(degree(Q)) + Q := reductum(Q) + return Q' + + qPowers (Xq:PolK, P:PolK) : PrimitiveArray(PolK) == -- Xq = X**q mod P + n := degree(P) + result : PrimitiveArray(PolK) := new(n, 1) + result(1) := Q := Xq + for i in 2 .. n-1 repeat (Q := Q*Xq rem P ; result(i) := Q) + return result + + discriminantTest?(P : PolK) : Boolean == + (delta : K := discriminant(P)) = 0 => true + StickelbergerTest : Boolean := (delta ** q' = 1) = even?(degree(P)) + return StickelbergerTest + + evenCharacteristicIrreducible?(P : PolK) : Boolean == + (n := degree(P)) = 0 => false + n = 1 => true + degree(gcd(P, D(P))) > 0 => false + if (lcP := leadingCoefficient(P)) ^= 1 then P := inv(lcP) * P + S : PolK := exp(X, q, P) + if degree(gcd(S - X, P)) > 0 then + return false + if n < 4 then return true + maxDegreeToTest : NonNegativeInteger := n quo 2 + XqPowers : PrimitiveArray(PolK) := qPowers(S, P) + for i in 2 .. maxDegreeToTest repeat + S := qExp(S, XqPowers) + if degree(gcd(S - X, P)) > 0 then + return false + return true + + oddCharacteristicIrreducible?(P : PolK) : Boolean == + (n := degree(P)) = 0 => false + n = 1 => true + discriminantTest?(P) => false + if (lcP := leadingCoefficient(P)) ^= 1 then P := inv(lcP) * P + S : PolK := exp(X, q, P) + if degree(gcd(S - X, P)) > 0 then + return false + if n < 6 then return true + maxDegreeToTest : NonNegativeInteger := n quo 3 + XqPowers : PrimitiveArray(PolK) := qPowers(S, P) + for i in 2 .. maxDegreeToTest repeat + S := qExp(S, XqPowers) + if degree(gcd(S - X, P)) > 0 then + return false + return true + if p = 2 then + irreducible?(P : PolK) : Boolean == evenCharacteristicIrreducible?(P) + else + irreducible?(P : PolK) : Boolean == oddCharacteristicIrreducible?(P) + +@ +<>= +"FFFACTSE" [color="#FF4488",href="bookvol10.4.pdf#nameddest=FFFACTSE"] +"FFSQFR" [color="#FF4488",href="bookvol10.4.pdf#nameddest=FFSQFR"] +"PFECAT" [color="#4488FF",href="bookvol10.2.pdf#nameddest=PFECAT"] +"FFFACTSE" -> "FFSQFR" +"FFFACTSE" -> "PFECAT" + +@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{package FFF FiniteFieldFunctions} \pagehead{FiniteFieldFunctions}{FFF} @@ -154004,6 +154283,7 @@ ZeroDimensionalSolvePackage(R,ls,ls2): Exports == Implementation where <> <> <> +<> <> <> <> diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index 344afd6..1fb01cf 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -23912,6 +23912,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. 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+20100421 tpd src/algebra/Makefile add FFFACTSE +20100421 tpd books/bookvol5.pamphlet add FFFACTSE +20100421 tpd books/ps/v104finitefieldfactorizationwithsizeparsebysideeffect.ps +20100421 tpd books/bookvol10.4 add FFFACTSE 20100420 tpd src/axiom-website/patches.html 20100420.01.tpd.patch 20100420 tpd zips/gcl-2.6.8pre4.unixport.makefile.patch 20100420 tpd zips/gcl-2.6.8pre4.unixport.init_gcl.lsp.in.patch diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 30afa87..fea2dab 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -8691,12 +8691,13 @@ LAYER11=\ @ \subsection{Layer12} -Depends on: DIOPS DPOLCAT FINRALG FRAC RMATCAT RRCC UPXSCAT\\ +Depends on: DIOPS DPOLCAT FINRALG FRAC RMATCAT RRCC UPXSCAT FFSQFR\\ Used by next layer: DIAGG FRAMALG MDAGG SMATCAT UPXSCCA <>= LAYER12=\ ${OUT}/DIAGG.o ${OUT}/DIAGG-.o ${OUT}/DSMP.o ${OUT}/EXPUPXS.o \ + ${OUT}/FFFACTSE.o \ ${OUT}/FRAMALG.o ${OUT}/FRAMALG-.o ${OUT}/MDAGG.o ${OUT}/ODPOL.o \ ${OUT}/PLOT.o ${OUT}/RMCAT2.o ${OUT}/ROIRC.o ${OUT}/SDPOL.o \ ${OUT}/SMATCAT.o ${OUT}/SMATCAT-.o ${OUT}/TUBETOOL.o ${OUT}/UPXSCCA.o \ @@ -8706,7 +8707,7 @@ LAYER12=\ @ <>= /* layer 12 */ -/* depends on: DIOPS DPOLCAT FINRALG FRAC RMATCAT RRCC UPXSCAT */ +/* depends on: DIOPS DPOLCAT FFSQFRFINRALG FRAC RMATCAT RRCC UPXSCAT */ "DFLOAT" [color="#88FF44",href="bookvol10.3.pdf#nameddest=DFLOAT", shape=ellipse] @@ -8767,6 +8768,28 @@ LAYER12=\ /*"EXPUPXS" -> {"EVALAB"; "IEVALAB"; "DIFEXT"; "FLINEXP"; "PATAB"; "FPATMAB"}*/ /*"EXPUPXS" -> {"TYPE"; "PFECAT"}*/ +"FFFACTSE" [color="#FF4488",href="bookvol10.4.pdf#nameddest=FFFACTSE"] +/*"FFFACTSE" -> {"FFIELDC"; "FPC"; "FIELD"; "EUCDOM"; "PID"}*/ +/*"FFFACTSE" -> {"GCDDOM"; "INTDOM"; "COMRING"; "RING"; "RNG"}*/ +/*"FFFACTSE" -> {"ABELGRP"; "CABMON"; "ABELMON"; "ABELSG"}*/ +/*"FFFACTSE" -> {"SETCAT"; "BASTYPE"; "KOERCE"; "SGROUP"}*/ +/*"FFFACTSE" -> {"MONOID"; "LMODULE"; "BMODULE"; "RMODULE"}*/ +/*"FFFACTSE" -> {"ALGEBRA"; "MODULE"; "ENTIRER"; "UFD"}*/ +/*"FFFACTSE" -> {"DIVRING"; "CHARNZ"; "FINITE"; "STEP"; "DIFRING"}*/ +/*"FFFACTSE" -> {"UPOLYC"; "POLYCAT"; "PDRING"; "FAMR"; "AMR"}*/ +/*"FFFACTSE" -> {"CHARZ"; "FRETRCT"; "RETRACT"; "EVALAB"}*/ +/*"FFFACTSE" -> {"IEVALAB"; "FLINEXP"; "LINEXP"; "ORDSET"}*/ +/*"FFFACTSE" -> {"KONVERT"; "PATMAB"}*/ +"FFFACTSE" -> "PFECAT" +"FFFACTSE" -> "FFSQFR" +/*"FFFACTSE" -> {"ELTAB"; "DIFEXT"}*/ +/*"FFFACTSE" -> {"NNI"; "INT"; "PI"; "PRIMARR"; "A1AGG"; "FLAGG"}*/ +/*"FFFACTSE" -> {"LNAGG"; "IXAGG"; "HOAGG"; "AGG"; "TYPE"}*/ +/*"FFFACTSE" -> {"ELTAGG"; "CLAGG"; "BOOLEAN"; "SINT"; "LIST"}*/ +/*"FFFACTSE" -> {"ILIST"; "LSAGG-"; "STAGG-"; "INS-"; "INS"}*/ +/*"FFFACTSE" -> {"OINTDOM"; "ORDRING"; "OAGROUP"; "OCAMON"}*/ +/*"FFFACTSE" -> {"OAMON"; "OASGP"; "CFCAT"; "REAL"}*/ + "FRAMALG" [color="#4488FF",href="bookvol10.2.pdf#nameddest=FRAMALG"] "FRAMALG" -> "FINRALG" /*"FRAMALG" -> {"ALGEBRA"; "RING"; "RNG"; "ABELGRP"; "CABMON"; "ABELMON"}*/ @@ -15572,6 +15595,7 @@ New algebra files can depend on new algebra files. Since these files are not part of the default database we need to be explicit about the new files being loaded with the library command. +This block of files is necessary to build the GUESS package. <>= FFFGFDEPS = FAMR2 FFFG @@ -15751,6 +15775,42 @@ ${MID}/GUESSUP.nrlib/code.o: ${MID}/GUESSUP.spad @ +This block of files is necessary to build the PAPP package. + +The domain FFFACTSE does an import of the domain FFSQFR in order to +get the Yun function. This works in the interpreter because FFSQFR is +already in the database after the build. At build time FFSQFR has already +been compiled but the import does not load the library. We could fix this +several ways. The optimal way seems to be to have the compimport function +load the NRLIB. A sub-optimal but successful compromise is to load the +required file by hand which we do here. Other alternative solutions might +be +\begin{itemize} +\item does bootstrap mode just compile headers? is that all we need? +\item we could add FFSQFR to the bootstrap layer. However, we are trying +to shrink and elimiate bootstrap code so this is not good. +\item we would rebuild the database after every layer. this eliminates +several problems but we need to investigate what it breaks. +\item we would rebuild the database after every compile. this eliminates +several problems but we need to investigate what it breaks. +\item as mentioned, we could have import do an implicit library call to +load the imported file if it is not already known. +\end{itemize} +<>= + +PAPPDEPS = FFSQFR + +${MID}/FFFACTSE.nrlib/code.o: ${MID}/FFFACTSE.spad + @echo P1 making ${MID}/FFFACTSE.nrlib/code.o from ${MID}/FFFACTSE.spad + @ (cd ${MID} ; \ + if [ -z "${NOISE}" ] ; then \ + echo -e ")lib ${PAPPDEPS} \n )co FFFACTSE.spad" | ${INTERPSYS} ; \ + else \ + echo -e ")lib ${PAPPDEPS} \n )co FFFACTSE.spad" \ + | ${INTERPSYS} >${TMP}/trace ; \ + fi ) + +@ \section{Broken Files} These files are Aldor files \begin{verbatim} @@ -16488,6 +16548,7 @@ SPADHELP=\ ${HELP}/FactoredFunctions2.help \ ${HELP}/File.help \ ${HELP}/FileName.help \ + ${HELP}/FiniteFieldFactorizationWithSizeParseBySideEffect.help \ ${HELP}/FiniteFieldSquareFreeDecomposition.help \ ${HELP}/FlexibleArray.help \ ${HELP}/Float.help \ @@ -16645,6 +16706,7 @@ REGRESS= \ FactoredFunctions2.regress \ File.regress \ FileName.regress \ + FiniteFieldFactorizationWithSizeParseBySideEffect.regress \ FiniteFieldSquareFreeDecomposition.regress \ FlexibleArray.regress \ Float.regress \ @@ -17101,6 +17163,23 @@ ${HELP}/FileName.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/FileName.input @echo "FileName (FNAME)" >>${HELPFILE} +${HELP}/FiniteFieldFactorizationWithSizeParseBySideEffect.help: \ + ${BOOKS}/bookvol10.4.pamphlet + @echo 7303 create \ + FiniteFieldFactorizationWithSizeParseBySideEffect.help from \ + ${BOOKS}/bookvol10.4.pamphlet + @${TANGLE} -R"FiniteFieldFactorizationWithSizeParseBySideEffect.help" \ + ${BOOKS}/bookvol10.4.pamphlet \ + >${HELP}/FiniteFieldFactorizationWithSizeParseBySideEffect.help + @cp ${HELP}/FiniteFieldFactorizationWithSizeParseBySideEffect.help \ + ${HELP}/FFFACTSE.help + @${TANGLE} \ + -R"FiniteFieldFactorizationWithSizeParseBySideEffect.input" \ + ${BOOKS}/bookvol10.4.pamphlet \ + >${INPUT}/FiniteFieldFactorizationWithSizeParseBySideEffect.input + @echo "FiniteFieldFactorizationWithSizeParseBySideEffect (FFFACTSE)"\ + >>${HELPFILE} + ${HELP}/FiniteFieldSquareFreeDecomposition.help: ${BOOKS}/bookvol10.4.pamphlet @echo 7305 create FiniteFieldSquareFreeDecomposition.help from \ ${BOOKS}/bookvol10.4.pamphlet diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 26c6afd..c6d2ba7 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2649,5 +2649,7 @@ books/bookvol10.3 improve UnivariateTaylorSeriesCZero docs
books/bookvol4 document how to make graphs in algebra books
20100420.01.tpd.patch zips/gcl-2.6.8pre4.tgz added, fix for ubuntu 9.10
+20100421.01.tpd.patch +books/bookvol10.4 add FiniteFieldFactorizationWithSizeParseBySideEffect