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: (UP -> UP, List Fraction UP -> List Record(ratpart: Fraction UP, coeffs: Vector F), (Fraction UP, List Fraction UP) -> List Record(ratpart: Fraction UP, coeffs: Vector F), Matrix F -> List Vector 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: (UP -> UP, Matrix F -> List Vector 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.