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## [Axiom-developer] [RationalInterpolation]

 From: Bill Page Subject: [Axiom-developer] [RationalInterpolation] Date: Mon, 21 Mar 2005 00:11:08 -0600

Changes
http://page.axiom-developer.org/zope/mathaction/RationalInterpolation/diff
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It requires the following previously compiled package:
\begin{axiom}
)lib RINTERPA
\end{axiom}

\begin{axiom}
f(x)== (x^3+5*x-3)/(x^2-3)
f(x)
xlist:List FRAC INT :=[1/2, 4, 1/6, 8, 1/10, 12]
ylist :=[f(x) for x in xlist]
\end{axiom}

A harder example:

\begin{axiom}
dom:=DMP([z],INT);
g:FRAC dom -> FRAC dom
g(x) == (x^3*z+5*z^2*x -3*z^3)/(z*x^2 - 3)
xxlist:List FRAC dom:=[1/(2*z), 4*z, 1/(6*z), 8*z, 1/(10*z), 12*z]
yylist:=[g(x) for x in xxlist]
--RationalInterpolation(xxlist, yylist, 3::NNI, 2::NNI)$RINTERPA(FRAC dom, UP(x, FRAC dom)) \end{axiom} \begin{axiom} interpolate(xlist, ylist, 3, 2)$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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