ParametricTranscendentalIntegration(F, UP)

intpar.spad line 466 [edit on github]

• F : Field
• UP : UnivariatePolynomialCategory(F)

This package implements parametric integration in transcendental case.

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

diffextint(ext, csolve, [g1, ..., gn]) is like primextint and expextint but for differentialy transcendental extensions.

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

expextint(', rde, csolve, [g1, ..., gn]) returns a basis of solution of the homogeneous system h' + c1*g1 + ... + cn*gn = 0 Argument foo is an parametric rde solver on F. csolve is solver over constants.

logextint : (Mapping(UP, UP), Mapping(Factored(UP), UP), Mapping(List(Vector(Fraction(Integer))), Matrix(F)), Mapping(Record(logands : List(Fraction(UP)), basis : List(Vector(Fraction(Integer)))), List(UP)), List(Fraction(UP))) -> Record(logands : List(Fraction(UP)), basis : List(Vector(Fraction(Integer))))

logextint(der, ufactor, csolve, rec, [g1, ..., gn]) returns [[u1, ..., um], bas] giving basis of solution of the homogeneous systym c1*g1 + ... + cn*gn + c_n+1u1'/u1 + ... c_n+mum'/um = 0

monologextint : (List(UP), Mapping(List(Vector(Fraction(Integer))), Matrix(F)), Mapping(Record(logands : List(F), basis : List(Vector(Fraction(Integer)))), List(F))) -> Record(logands : List(Fraction(UP)), basis : List(Vector(Fraction(Integer))))

monologextint(lup, csolve, rec) is a helper for logextint

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

primextint(', ext, 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. csolve is solver over constants.

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

unkextint(ext, csolve, [g1, ..., gn]) is like primextint and expextint but for makes no assumption about generator of the extension.