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## [Axiom-developer] [RationalInterpolationAlgorithms] Move back RationalIn

 From: wyscc Subject: [Axiom-developer] [RationalInterpolationAlgorithms] Move back RationalInterpolation; example, question Date: Sat, 19 Mar 2005 05:00:19 -0600

Changes
http://page.axiom-developer.org/zope/mathaction/RationalInterpolationAlgorithms/diff
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??changed:
-Next RationalInterpolation
-
The package below implements rational interpolation.
\begin{axiom}
)abbrev package RINTERP RationalInterpolation
++ Description:
++ This package exports interpolation algorithms
RationalInterpolation(xx, F): Cat == Body   where
xx: Symbol
F:  IntegralDomain
UP  ==> UnivariatePolynomial
SUP ==> SparseUnivariatePolynomial

Cat == with
interpolate: (Fraction UP(xx, F), List F, List F, _
NonNegativeInteger, NonNegativeInteger) _
-> Fraction UP(xx, F)
interpolate: (List F, List F, NonNegativeInteger, NonNegativeInteger) _
-> Fraction SUP F

RIA ==> RationalInterpolationAlgorithms

interpolate(qx, lx, ly, m, k) ==
px := RationalInterpolation(lx, ly, m, k)$RIA(F, UP(xx, F)) elt(px, qx) interpolate(lx, ly, m, k) == RationalInterpolation(lx, ly, m, k)$RIA(F, SUP F)
\end{axiom}

Comments: Packages compiled on MathAction seems to be local to the page.
Dependent packages therefore needs to be on the same page to load the packages
in correct sequence.

Example:

\begin{axiom}
interpolate(xlist, ylist, 3, 2)$RINTERP('x, FRAC INT) interpolate(1/6::FRAC UP(x,FRAC INT), xlist, ylist, 3,2)$RINTERP('x,FRAC INT)
interpolate(xxlist, yylist, 3, 2)$RINTERP('x, FRAC dom) interpolate(4*z::FRAC UP(x,dom), xxlist, yylist, 3, 2)$RINTERP('x, FRAC dom)
\end{axiom}

Question: If <code>p(xx) = interpolate(lx, ly, m, k)</code>, what is the
purpose of
<code>elt(px, qx) = p(qx)</code>, the composition of <code>p(xx)</code> and
<code>qx</code>, especially when <code>qx</code> is from <code>FRAC UP(xx,
F)</code> instead of from just <code>F</code>? and why is this function (the
composition) also called <code>interpolate</code>?

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