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diff --git a/src/algebra/pinterp.spad.pamphlet b/src/algebra/pinterp.spad.pamphlet new file mode 100644 index 00000000..d8c1482f --- /dev/null +++ b/src/algebra/pinterp.spad.pamphlet @@ -0,0 +1,111 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra pinterp.spad} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{package PINTERPA PolynomialInterpolationAlgorithms} +<<package PINTERPA PolynomialInterpolationAlgorithms>>= +)abbrev package PINTERPA PolynomialInterpolationAlgorithms +++ Description: +++ This package exports interpolation algorithms +PolynomialInterpolationAlgorithms(F, P): Cat == Body where + F: Field + P: UnivariatePolynomialCategory(F) + + Cat ==> with + LagrangeInterpolation: (List F, List F) -> P + ++ LagrangeInterpolation(l1,l2) \undocumented + + Body ==> add + LagrangeInterpolation(lx, ly) == + #lx ^= #ly => + error "Different number of points and values." + ip: P := 0 + for xi in lx for yi in ly for i in 0.. repeat + pp: P := 1 + xp: F := 1 + for xj in lx for j in 0.. | i ^= j repeat + pp := pp * (monomial(1,1) - monomial(xj,0)) + xp := xp * (xi - xj) + ip := ip + (yi/xp) * pp + ip + +@ +\section{package PINTERP PolynomialInterpolation} +<<package PINTERP PolynomialInterpolation>>= +)abbrev package PINTERP PolynomialInterpolation +++ Description: +++ This package exports interpolation algorithms +PolynomialInterpolation(xx, F): Cat == Body where + xx: Symbol + F: Field + UP ==> UnivariatePolynomial + SUP ==> SparseUnivariatePolynomial + + Cat ==> with + interpolate: (UP(xx,F), List F, List F) -> UP(xx,F) + ++ interpolate(u,lf,lg) \undocumented + interpolate: (List F, List F) -> SUP F + ++ interpolate(lf,lg) \undocumented + + Body ==> add + PIA ==> PolynomialInterpolationAlgorithms + + interpolate(qx, lx, ly) == + px := LagrangeInterpolation(lx, ly)$PIA(F, UP(xx, F)) + elt(px, qx) + + interpolate(lx, ly) == + LagrangeInterpolation(lx, ly)$PIA(F, SUP F) + +@ +\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 PINTERPA PolynomialInterpolationAlgorithms>> +<<package PINTERP PolynomialInterpolation>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |