FractionFreeFastGaussianFractions(D, V, VF)

fffg.spad line 525 [edit on github]

• D : Join(IntegralDomain, GcdDomain)
• V : FiniteAbelianMonoidRing(D, NonNegativeInteger)
• VF : FiniteAbelianMonoidRing(Fraction(D), NonNegativeInteger)

This package lifts the interpolation functions from FractionFreeFastGaussian to fractions.

generalInterpolation : (List(D), Mapping(D, NonNegativeInteger, NonNegativeInteger, V), Vector(VF), List(NonNegativeInteger)) -> Matrix(SparseUnivariatePolynomial(D))

generalInterpolation(l, CA, f, eta) performs Hermite-Pade approximation using the given action CA of polynomials on the elements of f. The result is guaranteed to be correct up to order |eta|-1. Given that eta is a "normal" point, the degrees on the diagonal are given by eta. The degrees of column i are in this case eta + e.i - [1, 1, ..., 1], where the degree of zero is -1.