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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra poltopol.spad}
\author{Manuel Bronstein, Patrizia Gianni}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package MPC2 MPolyCatFunctions2}
<<package MPC2 MPolyCatFunctions2>>=
)abbrev package MPC2 MPolyCatFunctions2
++ Utilities for MPolyCat
++ Author: Manuel Bronstein
++ Date Created: 1987
++ Date Last Updated: 28 March 1990 (PG)
MPolyCatFunctions2(VarSet,E1,E2,R,S,PR,PS) : public == private where
VarSet : OrderedSet
E1 : OrderedAbelianMonoidSup
E2 : OrderedAbelianMonoidSup
R : Ring
S : Ring
PR : PolynomialCategory(R,E1,VarSet)
PS : PolynomialCategory(S,E2,VarSet)
SUPR ==> SparseUnivariatePolynomial PR
SUPS ==> SparseUnivariatePolynomial PS
public == with
map: (R -> S,PR) -> PS
++ map(f,p) \undocumented
reshape: (List S, PR) -> PS
++ reshape(l,p) \undocumented
private == add
supMap: (R -> S, SUPR) -> SUPS
supMap(fn : R -> S, supr : SUPR): SUPS ==
supr = 0 => monomial(fn(0$R) :: PS,0)$SUPS
c : PS := map(fn,leadingCoefficient supr)$%
monomial(c,degree supr)$SUPS + supMap(fn, reductum supr)
map(fn : R -> S, pr : PR): PS ==
varu : Union(VarSet,"failed") := mainVariable pr
varu case "failed" => -- have a constant
fn(retract pr) :: PS
var : VarSet := varu :: VarSet
supr : SUPR := univariate(pr,var)$PR
multivariate(supMap(fn,supr),var)$PS
@
\section{package MPC3 MPolyCatFunctions3}
<<package MPC3 MPolyCatFunctions3>>=
)abbrev package MPC3 MPolyCatFunctions3
++ Description:
++ This package \undocumented
MPolyCatFunctions3(Vars1,Vars2,E1,E2,R,PR1,PR2): C == T where
E1 : OrderedAbelianMonoidSup
E2 : OrderedAbelianMonoidSup
Vars1: OrderedSet
Vars2: OrderedSet
R : Ring
PR1 : PolynomialCategory(R,E1,Vars1)
PR2 : PolynomialCategory(R,E2,Vars2)
C ==> with
map: (Vars1 -> Vars2, PR1) -> PR2
++ map(f,x) \undocumented
T ==> add
map(f:Vars1 -> Vars2, p:PR1):PR2 ==
(x1 := mainVariable p) case "failed" =>
c:R:=(retract p)
c::PR2
up := univariate(p, x1::Vars1)
x2 := f(x1::Vars1)
ans:PR2 := 0
while up ~= 0 repeat
ans := ans + monomial(map(f,leadingCoefficient up),x2,degree up)
up := reductum up
ans
@
\section{package POLTOPOL PolToPol}
<<package POLTOPOL PolToPol>>=
)abbrev package POLTOPOL PolToPol
++ Author : P.Gianni, Summer '88
++ Description:
++ Package with the conversion functions among different kind of polynomials
PolToPol(lv,R) : C == T
where
R : Ring
lv : List Symbol
NNI ==> NonNegativeInteger
Ov ==> OrderedVariableList(lv)
IES ==> IndexedExponents Symbol
DP ==> DirectProduct(#lv,NonNegativeInteger)
DPoly ==> DistributedMultivariatePolynomial(lv,R)
HDP ==> HomogeneousDirectProduct(#lv,NonNegativeInteger)
HDPoly ==> HomogeneousDistributedMultivariatePolynomial(lv,R)
P ==> Polynomial R
VV ==> Vector NNI
MPC3 ==> MPolyCatFunctions3
C == with
dmpToHdmp : DPoly -> HDPoly
++ dmpToHdmp(p) converts p from a \spadtype{DMP} to a \spadtype{HDMP}.
hdmpToDmp : HDPoly -> DPoly
++ hdmpToDmp(p) converts p from a \spadtype{HDMP} to a \spadtype{DMP}.
pToHdmp : P -> HDPoly
++ pToHdmp(p) converts p from a \spadtype{POLY} to a \spadtype{HDMP}.
hdmpToP : HDPoly -> P
++ hdmpToP(p) converts p from a \spadtype{HDMP} to a \spadtype{POLY}.
dmpToP : DPoly -> P
++ dmpToP(p) converts p from a \spadtype{DMP} to a \spadtype{POLY}.
pToDmp : P -> DPoly
++ pToDmp(p) converts p from a \spadtype{POLY} to a \spadtype{DMP}.
T == add
variable1(xx:Symbol):Ov == variable(xx)::Ov
-- transform a P in a HDPoly --
pToHdmp(pol:P) : HDPoly ==
map(variable1,pol)$MPC3(Symbol,Ov,IES,HDP,R,P,HDPoly)
-- transform an HDPoly in a P --
hdmpToP(hdpol:HDPoly) : P ==
map(convert,hdpol)$MPC3(Ov,Symbol,HDP,IES,R,HDPoly,P)
-- transform an DPoly in a P --
dmpToP(dpol:DPoly) : P ==
map(convert,dpol)$MPC3(Ov,Symbol,DP,IES,R,DPoly,P)
-- transform a P in a DPoly --
pToDmp(pol:P) : DPoly ==
map(variable1,pol)$MPC3(Symbol,Ov,IES,DP,R,P,DPoly)
-- transform a DPoly in a HDPoly --
dmpToHdmp(dpol:DPoly) : HDPoly ==
dpol=0 => 0$HDPoly
monomial(leadingCoefficient dpol,
directProduct(degree(dpol)::VV)$HDP)$HDPoly+
dmpToHdmp(reductum dpol)
-- transform a HDPoly in a DPoly --
hdmpToDmp(hdpol:HDPoly) : DPoly ==
hdpol=0 => 0$DPoly
dd:DP:= directProduct((degree hdpol)::VV)$DP
monomial(leadingCoefficient hdpol,dd)$DPoly+
hdmpToDmp(reductum hdpol)
@
\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 MPC2 MPolyCatFunctions2>>
<<package MPC3 MPolyCatFunctions3>>
<<package POLTOPOL PolToPol>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
