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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra supxs.spad}
\author{Clifton J. Williamson}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain SUPXS SparseUnivariatePuiseuxSeries}
<<domain SUPXS SparseUnivariatePuiseuxSeries>>=
)abbrev domain SUPXS SparseUnivariatePuiseuxSeries
++ Author: Clifton J. Williamson
++ Date Created: 11 November 1994
++ Date Last Updated: June 18, 2010
++ Basic Operations:
++ Related Domains: InnerSparseUnivariatePowerSeries,
++ SparseUnivariateTaylorSeries, SparseUnivariateLaurentSeries
++ Also See:
++ AMS Classifications:
++ Keywords: sparse, series
++ Examples:
++ References:
++ Description: Sparse Puiseux series in one variable
++ \spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux
++ series in one variable with coefficients in an arbitrary ring. The
++ parameters of the type specify the coefficient ring, the power series
++ variable, and the center of the power series expansion. For example,
++ \spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux
++ series in \spad{(x - 3)} with \spadtype{Integer} coefficients.
SparseUnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
Coef : Ring
var : Symbol
cen : Coef
I ==> Integer
NNI ==> NonNegativeInteger
OUT ==> OutputForm
RN ==> Fraction Integer
SUTS ==> SparseUnivariateTaylorSeries(Coef,var,cen)
SULS ==> SparseUnivariateLaurentSeries(Coef,var,cen)
SUPS ==> InnerSparseUnivariatePowerSeries(Coef)
Exports ==> Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,SULS),_
PartialDifferentialDomain(%,Variable var),_
RetractableTo SUTS,CoercibleFrom Variable var) with
if Coef has Algebra Fraction Integer then
integrate: (%,Variable(var)) -> %
++ \spad{integrate(f(x))} returns an anti-derivative of the power
++ series \spad{f(x)} with constant coefficient 0.
++ We may integrate a series when we can divide coefficients
++ by integers.
Implementation ==> UnivariatePuiseuxSeriesConstructor(Coef,SULS) add
Rep := Record(expon:RN,lSeries:SULS)
getExpon: % -> RN
getExpon pxs == pxs.expon
variable x == var
center x == cen
coerce(v: Variable(var)) ==
zero? cen => monomial(1,1)
monomial(1,1) + monomial(cen,0)
coerce(uts:SUTS) == uts :: SULS :: %
retractIfCan(upxs:%):Union(SUTS,"failed") ==
(uls := retractIfCan(upxs)@Union(SULS,"failed")) case "failed" =>
"failed"
retractIfCan(uls :: SULS)@Union(SUTS,"failed")
if Coef has "*": (Fraction Integer, Coef) -> Coef then
differentiate(upxs:%,v:Variable(var)) == differentiate upxs
if Coef has Algebra Fraction Integer then
integrate(upxs:%,v:Variable(var)) == integrate upxs
--% OutputForms
coerce(x:%): OUT ==
sups : SUPS := laurentRep(x) pretend SUPS
st := getStream sups; refer := getRef sups
if not(explicitlyEmpty? st or explicitEntries? st) _
and (nx := retractIfCan(deref refer)@Union(I,"failed")) case I then
count : NNI := _$streamCount$Lisp
degr := min(count,(nx :: I) + count + 1)
extend(sups,degr)
seriesToOutputForm(st,refer,variable x,center x,rationalPower x)
@
\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>>
<<domain SUPXS SparseUnivariatePuiseuxSeries>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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