ParametricTranscendentalIntegration(F, UP)¶

This package implements parametric integration in transcendental case.

diffextint: (List UP -> List Record(ratpart: F, coeffs: Vector F), Matrix F -> List Vector 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: (UP -> UP, (Integer, List F) -> List Record(ratpart: F, coeffs: Vector F), Matrix F -> List Vector 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: (UP -> UP, UP -> Factored UP, Matrix F -> List Vector Fraction Integer, List UP -> Record(logands: List Fraction UP, basis: List Vector Fraction Integer), 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+1}u1'/u1 + ... c_{n+m}um'/um = 0`

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

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

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