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”.