TranscendentalRischDESystem(F, UP)

rdesys.spad line 1 [edit on github]

Risch differential equation system, transcendental case. Author: Manuel Bronstein Date Created: 17 August 1992

baseRDEsys: (Fraction UP, Fraction UP, Fraction UP) -> Union(List Fraction UP, failed)

baseRDEsys(f, g1, g2) returns fractions y_1.y_2 such that (y1', y2') + ((0, -f), (f, 0)) (y1, y2) = (g1, g2) if y_1,y_2 exist, “failed” otherwise.

monomRDEsys: (Fraction UP, Fraction UP, Fraction UP, UP -> UP) -> Union(Record(a: UP, b: Fraction UP, h: UP, c1: Fraction UP, c2: Fraction UP, t: UP), failed)

monomRDEsys(f, g1, g2, D) returns [A, B, H, C1, C2, T] such that (y1', y2') + ((0, -f), (f, 0)) (y1, y2) = (g1, g2) has a solution if and only if y1 = Q1 / T, y2 = Q2 / T, where B, C1, C2, Q1, Q2 have no normal poles and satisfy A (Q1', Q2') + ((H, -B), (B, H)) (Q1, Q2) = (C1, C2) D is the derivation to use.