PadeApproximantPackage(R, x, pt)

pade.spad line 1 [edit on github]

• R : Field
• x : Symbol
• pt : R

This package computes reliable Pade approximants using a generalized Viskovatov continued fraction algorithm.

pade : (NonNegativeInteger, NonNegativeInteger, UnivariateTaylorSeries(R, x, pt)) -> Union(Fraction(UnivariatePolynomial(x, R)), "failed")

pade(nd, dd, s) computes the quotient of polynomials (if it exists) with numerator degree at most nd and denominator degree at most dd which matches the series s to order nd + dd.

pade : (NonNegativeInteger, NonNegativeInteger, UnivariateTaylorSeries(R, x, pt), UnivariateTaylorSeries(R, x, pt)) -> Union(Fraction(UnivariatePolynomial(x, R)), "failed")

pade(nd, dd, ns, ds) computes the approximant as a quotient of polynomials (if it exists) for arguments nd (numerator degree of approximant), dd (denominator degree of approximant), ns (numerator series of function), and ds (denominator series of function).