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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra gseries.spad}
\author{Clifton J. Williamson}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain GSERIES GeneralUnivariatePowerSeries}
<<domain GSERIES GeneralUnivariatePowerSeries>>=
)abbrev domain GSERIES GeneralUnivariatePowerSeries
++ Author: Clifton J. Williamson
++ Date Created: 22 September 1993
++ Date Last Updated: June 18, 2010
++ Basic Operations:
++ Related Domains:
++ Also See:
++ AMS Classifications:
++ Keywords: series, Puiseux
++ Examples:
++ References:
++ Description:
++ This is a category of univariate Puiseux series constructed
++ from univariate Laurent series. A Puiseux series is represented
++ by a pair \spad{[r,f(x)]}, where r is a positive rational number and
++ \spad{f(x)} is a Laurent series. This pair represents the Puiseux
++ series \spad{f(x\^r)}.
GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where
Coef : Ring
var : Symbol
cen : Coef
I ==> Integer
UTS ==> UnivariateTaylorSeries
ULS ==> UnivariateLaurentSeries
UPXS ==> UnivariatePuiseuxSeries
EFULS ==> ElementaryFunctionsUnivariateLaurentSeries
EFUPXS ==> ElementaryFunctionsUnivariatePuiseuxSeries
FS2UPS ==> FunctionSpaceToUnivariatePowerSeries
Exports ==> Join(UnivariatePuiseuxSeriesCategory Coef,_
PartialDifferentialDomain(%,Variable var)) with
coerce: Variable(var) -> %
++ coerce(var) converts the series variable \spad{var} into a
++ Puiseux series.
coerce: UPXS(Coef,var,cen) -> %
++ coerce(f) converts a Puiseux series to a general power series.
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 ==> UnivariatePuiseuxSeries(Coef,var,cen) add
coerce(upxs:UPXS(Coef,var,cen)) == upxs pretend %
puiseux: % -> UPXS(Coef,var,cen)
puiseux f == f pretend UPXS(Coef,var,cen)
if Coef has Algebra Fraction Integer then
differentiate f ==
str1 : String := "'differentiate' unavailable on this domain; "
str2 : String := "use 'approximate' first"
error concat(str1,str2)
differentiate(f:%,v:Variable(var)) == differentiate f
if Coef has PartialDifferentialRing(Symbol) then
differentiate(f:%,s:Symbol) ==
(s = variable(f)) =>
str1 : String := "'differentiate' unavailable on this domain; "
str2 : String := "use 'approximate' first"
error concat(str1,str2)
dcds := differentiate(center f,s)
deriv := differentiate(puiseux f) :: %
map(differentiate(#1,s),f) - dcds * deriv
integrate f ==
str1 : String := "'integrate' unavailable on this domain; "
str2 : String := "use 'approximate' first"
error concat(str1,str2)
integrate(f:%,v:Variable(var)) == integrate f
if Coef has integrate: (Coef,Symbol) -> Coef and _
Coef has variables: Coef -> List Symbol then
integrate(f:%,s:Symbol) ==
(s = variable(f)) =>
str1 : String := "'integrate' unavailable on this domain; "
str2 : String := "use 'approximate' first"
error concat(str1,str2)
not entry?(s,variables center f) => map(integrate(#1,s),f)
error "integrate: center is a function of variable of integration"
if Coef has TranscendentalFunctionCategory and _
Coef has PrimitiveFunctionCategory and _
Coef has AlgebraicallyClosedFunctionSpace Integer then
integrateWithOneAnswer: (Coef,Symbol) -> Coef
integrateWithOneAnswer(f,s) ==
res := integrate(f,s)$FunctionSpaceIntegration(Integer,Coef)
res case Coef => res :: Coef
first(res :: List Coef)
integrate(f:%,s:Symbol) ==
(s = variable(f)) =>
str1 : String := "'integrate' unavailable on this domain; "
str2 : String := "use 'approximate' first"
error concat(str1,str2)
not entry?(s,variables center f) =>
map(integrateWithOneAnswer(#1,s),f)
error "integrate: center is a function of variable of integration"
@
\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 GSERIES GeneralUnivariatePowerSeries>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
