[Axiom-developer] [Experiment #2]

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Changes http://page.axiom-developer.org/zope/mathaction/Experiment2/diff
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??changed:
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\begin{axiom}
)abbrev package RINTERPA RationalInterpolationAlgorithms
++ Description:
++ This package exports rational interpolation algorithms
RationalInterpolationAlgorithms(F, P): Cat == Body   where
    F: IntegralDomain 
    P: UnivariatePolynomialCategory(F)
    Cat == with
        RationalInterpolation: (List F, List F, NonNegativeInteger,
                                NonNegativeInteger) 
                               -> Fraction P
        +++ We assume that the elements of the first list are all distinct.
        +++ If they are not, division by zero might occur.

    Body == add
        RationalInterpolation(xlist, ylist, m, k) ==
            #xlist ^= #ylist =>
                error "Different number of points and values."
            #xlist ^= m+k+1 =>
                error "wrong number of points"
            tempvec: List F := [1 for i in 1..(m+k+1)]

            collist: List List F := cons(tempvec, 
                                         [(tempvec := [tempvec.i * xlist.i _
                                                       for i in 1..(m+k+1)]) _
                                          for j in 1..max(m, k)])

            collist := append([collist.j for j in 1..(m+1)], _
                              [[- collist.j.i * ylist.i for i in 1..(m+k+1)] _
                               for j in 1..(k+1)])
            resspace: List Vector F := nullSpace((transpose matrix collist) _
                                                 ::Matrix F)
            reslist: List List P := _
                      [[monomial((resspace.1).(i+1), i) for i in 0..m], _
                      [monomial((resspace.1).(i+m+2), i) for i in 0..k]]

            reduce((_+), reslist.1)/reduce((_+), reslist.2)
\end{axiom}

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