AlgebraicIntegration(R, F)

intaf.spad line 708 [edit on github]

• R: Join(Comparable, IntegralDomain)

• F: Join(AlgebraicallyClosedField, FunctionSpace R)

This package provides functions for the integration of algebraic integrands over transcendental functions.

algextint: (Kernel F, Kernel F, SparseUnivariatePolynomial F -> SparseUnivariatePolynomial F, List Fraction SparseUnivariatePolynomial F -> List Record(ratpart: Fraction SparseUnivariatePolynomial F, coeffs: Vector F), (Fraction SparseUnivariatePolynomial F, List Fraction SparseUnivariatePolynomial F) -> List Record(ratpart: Fraction SparseUnivariatePolynomial F, coeffs: Vector F), Matrix F -> List Vector F, List F) -> List Record(ratpart: F, coeffs: Vector F)

algextint(x, y, d, ext, rde, csolve, [g1, ..., gn]) returns [h, [c1, ..., cn]] such that f = dh/dx + sum(ci gi) and dci/dx = 0, if such [h, [c1, ..., cn]] exist, “failed” otherwise.

algextint_base: (Kernel F, Kernel F, SparseUnivariatePolynomial F -> SparseUnivariatePolynomial F, Matrix F -> List Vector F, List F) -> List Record(ratpart: F, coeffs: Vector F)

algextint_base(x, y, d, csolve, [g1, ..., gn]) is like algextint but assumes that y and gi-s are purely algebraic

algint: (F, Kernel F, Kernel F, SparseUnivariatePolynomial F -> SparseUnivariatePolynomial F, F -> IntegrationResult F) -> IntegrationResult F

algint(f, x, y, d) returns the integral of f(x, y)dx where y is an algebraic function of x; d is the derivation to use on k[x].