[Top][All Lists]

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[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


-Next RationalInterpolation
The package below implements rational interpolation. 
)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

    Body == add
        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)

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.


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)

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>?

forwarded from

reply via email to

[Prev in Thread] Current Thread [Next in Thread]