InnerModularHermitePade

modhpsol.spad line 359 [edit on github]

This package solves Hermite-Pade interpolation problem over ring of integer polynomials.We use reduction modulo primes and modular reconstruction to reduce problem to polynomials modulo $Z_p$.Then we use evaluation and Lagrange interpolation to reduce problem to solving over $Z_p$.

do_modular_solve : (Vector(U32Vector), Vector(Integer), NonNegativeInteger, U32Vector, Integer, Symbol) -> Union(Record(basis : TwoDimensionalArray(U32Vector), defects : Vector(Integer), cinds : Vector(Integer)), "no_solution")

do_poly_integer : (List(Symbol), List(PrimitiveArray(Fraction(Polynomial(Integer)))), Vector(Integer), NonNegativeInteger, U32Vector, Symbol, Symbol, Mapping(Vector(U32Vector), List(U32Vector), Integer, Integer)) -> Union(Record(defects : Vector(Integer), cinds : Vector(Integer), rowlen : Integer, offsetdata : Vector(Integer), expdata : SortedExponentVector, coeffdata : PrimitiveArray(Integer)), "no_solution")

merge2 : (Integer, List(Integer), List(Integer), Vector(Integer), SortedExponentVector, Vector(Integer), SortedExponentVector) -> Record(offsetdata : Vector(Integer), expdata : SortedExponentVector)

merge_exponents : (Integer, Vector(Integer), SortedExponentVector, Vector(Integer), SortedExponentVector) -> List(List(Integer))