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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra funcpkgs.spad}
\author{Manuel Bronstein}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package FSUPFACT FunctionSpaceUnivariatePolynomialFactor}
<<package FSUPFACT FunctionSpaceUnivariatePolynomialFactor>>=
)abbrev package FSUPFACT FunctionSpaceUnivariatePolynomialFactor
++ Used internally by IR2F
++ Author: Manuel Bronstein
++ Date Created: 12 May 1988
++ Date Last Updated: 22 September 1993
++ Keywords: function, space, polynomial, factoring
FunctionSpaceUnivariatePolynomialFactor(R, F, UP):
Exports == Implementation where
R : Join(IntegralDomain, RetractableTo Integer)
F : FunctionSpace R
UP: UnivariatePolynomialCategory F
Q ==> Fraction Integer
K ==> Kernel F
AN ==> AlgebraicNumber
PQ ==> SparseMultivariatePolynomial(Q, K)
PR ==> SparseMultivariatePolynomial(R, K)
UPQ ==> SparseUnivariatePolynomial Q
UPA ==> SparseUnivariatePolynomial AN
FR ==> Factored UP
FRQ ==> Factored UPQ
FRA ==> Factored UPA
Exports ==> with
ffactor: UP -> FR
++ ffactor(p) tries to factor a univariate polynomial p over F
qfactor: UP -> Union(FRQ, "failed")
++ qfactor(p) tries to factor p over fractions of integers,
++ returning "failed" if it cannot
UP2ifCan: UP -> Union(overq: UPQ, overan: UPA, failed: Boolean)
++ UP2ifCan(x) should be local but conditional.
if F has RetractableTo AN then
anfactor: UP -> Union(FRA, "failed")
++ anfactor(p) tries to factor p over algebraic numbers,
++ returning "failed" if it cannot
Implementation ==> add
import AlgFactor(UPA)
import RationalFactorize(UPQ)
P2QifCan : PR -> Union(PQ, "failed")
UPQ2UP : (SparseUnivariatePolynomial PQ, F) -> UP
PQ2F : (PQ, F) -> F
ffactor0 : UP -> FR
dummy := kernel(new()$Symbol)$K
if F has RetractableTo AN then
UPAN2F: UPA -> UP
UPQ2AN: UPQ -> UPA
UPAN2F p ==
map(#1::F, p)$UnivariatePolynomialCategoryFunctions2(AN,UPA,F,UP)
UPQ2AN p ==
map(#1::AN, p)$UnivariatePolynomialCategoryFunctions2(Q,UPQ,AN,UPA)
ffactor p ==
(pq := anfactor p) case FRA =>
map(UPAN2F, pq::FRA)$FactoredFunctions2(UPA, UP)
ffactor0 p
anfactor p ==
(q := UP2ifCan p) case overq =>
map(UPQ2AN, factor(q.overq))$FactoredFunctions2(UPQ, UPA)
q case overan => factor(q.overan)
"failed"
UP2ifCan p ==
ansq := 0$UPQ ; ansa := 0$UPA
goforq? := true
while p ~= 0 repeat
if goforq? then
rq := retractIfCan(leadingCoefficient p)@Union(Q, "failed")
if rq case Q then
ansq := ansq + monomial(rq::Q, degree p)
ansa := ansa + monomial(rq::Q::AN, degree p)
else
goforq? := false
ra := retractIfCan(leadingCoefficient p)@Union(AN, "failed")
if ra case AN then ansa := ansa + monomial(ra::AN, degree p)
else return [true]
else
ra := retractIfCan(leadingCoefficient p)@Union(AN, "failed")
if ra case AN then ansa := ansa + monomial(ra::AN, degree p)
else return [true]
p := reductum p
goforq? => [ansq]
[ansa]
else
UPQ2F: UPQ -> UP
UPQ2F p ==
map(#1::F, p)$UnivariatePolynomialCategoryFunctions2(Q,UPQ,F,UP)
ffactor p ==
(pq := qfactor p) case FRQ =>
map(UPQ2F, pq::FRQ)$FactoredFunctions2(UPQ, UP)
ffactor0 p
UP2ifCan p ==
ansq := 0$UPQ
while p ~= 0 repeat
rq := retractIfCan(leadingCoefficient p)@Union(Q, "failed")
if rq case Q then ansq := ansq + monomial(rq::Q, degree p)
else return [true]
p := reductum p
[ansq]
ffactor0 p ==
smp := numer(ep := p(dummy::F))
(q := P2QifCan smp) case "failed" => p::FR
map(UPQ2UP(univariate(#1, dummy), denom(ep)::F), factor(q::PQ
)$MRationalFactorize(IndexedExponents K, K, Integer,
PQ))$FactoredFunctions2(PQ, UP)
UPQ2UP(p, d) ==
map(PQ2F(#1, d), p)$UnivariatePolynomialCategoryFunctions2(PQ,
SparseUnivariatePolynomial PQ, F, UP)
PQ2F(p, d) ==
map(#1::F, #1::F, p)$PolynomialCategoryLifting(IndexedExponents K,
K, Q, PQ, F) / d
qfactor p ==
(q := UP2ifCan p) case overq => factor(q.overq)
"failed"
P2QifCan p ==
and/[retractIfCan(c::F)@Union(Q, "failed") case Q
for c in coefficients p] =>
map(#1::PQ, retract(#1::F)@Q :: PQ,
p)$PolynomialCategoryLifting(IndexedExponents K,K,R,PR,PQ)
"failed"
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - Redistributions in binary form must reproduce the above copyright
-- notice, this list of conditions and the following disclaimer in
-- the documentation and/or other materials provided with the
-- distribution.
--
-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>
<<package FSUPFACT FunctionSpaceUnivariatePolynomialFactor>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
