AlgebraicIntegrate2(R0, F, UP, UPUP, R)

intpar.spad line 1441 [edit on github]

• R0 : Join(Comparable, IntegralDomain, RetractableTo(Integer))
• F : Join(AlgebraicallyClosedField, FunctionSpace(R0))
• UP : UnivariatePolynomialCategory(F)
• UPUP : UnivariatePolynomialCategory(Fraction(UP))
• R : FunctionFieldCategory(F, UP, UPUP)

This package implements parametric integration in algebraic case.Some cases remain unimplemented and the code throws errors when they appear as the input.

algextint : (Mapping(UP, UP), Mapping(List(Record(ratpart : Fraction(UP), coeffs : Vector(F))), List(Fraction(UP))), Mapping(List(Record(ratpart : Fraction(UP), coeffs : Vector(F))), Fraction(UP), List(Fraction(UP))), Mapping(List(Vector(F)), Matrix(F)), List(R)) -> List(Record(ratpart : R, coeffs : Vector(F)))

algextint(der, ext, rde, csolve, [g1, ..., gn]) returns a basis of solutions of the homogeneous system h' + c1*g1 + ... + cn*gn = 0. Argument ext is an extended integration function on F, rde is RDE solver, csolve is linear solver over constants.

algextint_base : (Mapping(UP, UP), Mapping(List(Vector(F)), Matrix(F)), List(R)) -> List(Record(ratpart : R, coeffs : Vector(F)))

algextint_base(der, csolve, [g1, ..., gn]) is like algextint(der, ext, rde, csolve, [g1, ..., gn]), but assumes that field is algebraic extension of rational functions and that gi-s have no poles at infinity.