DenominatorIntegration(R, F)

intden.spad line 28 [edit on github]

• R : Join(GcdDomain, Comparable, CharacteristicZero, RetractableTo(Integer), LinearlyExplicitOver(Integer))
• F : Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, LiouvillianFunctionCategory, SpecialFunctionCategory, FunctionSpace(R))

This package generates logarithmic integrals and polylogs corresponding to denominator of the integrand.

li_int : (Fraction(SparseUnivariatePolynomial(F)), Kernel(F), Symbol) -> Record(answer : Fraction(SparseUnivariatePolynomial(F)), logpart : Fraction(SparseUnivariatePolynomial(F)), ir : IntegrationResult(Fraction(SparseUnivariatePolynomial(F))))

li_int(f, k, x) generates logarithmic integrals.

poly_int : (Fraction(SparseUnivariatePolynomial(F)), Kernel(F), Symbol) -> Record(answer : Fraction(SparseUnivariatePolynomial(F)), logpart : Fraction(SparseUnivariatePolynomial(F)), ir : IntegrationResult(Fraction(SparseUnivariatePolynomial(F))))

poly_int(f, k, x) generates polylogarithms.

solve_u : (F, F, Symbol) -> Union(List(List(F)), "failed")

solve_u(f1, u, x) returns [[c1, k1], ..., [cn, kn]] such that f1 = c1*u^k1 + ... + cn^kn and D(ci, x) = 0 or "failed".