/usr/lib/open-axiom/src/algebra/pinterp.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
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)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
)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)
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