TranscendentalHermiteIntegration(F, UP)

intrf.spad line 213 [edit on github]

• F: Field

• UP: UnivariatePolynomialCategory F

Hermite integration, transcendental case.

HermiteIntegrate: (Fraction UP, UP -> UP) -> Record(answer: Fraction UP, logpart: Fraction UP, specpart: Fraction UP, polypart: UP)

HermiteIntegrate(f, D) returns [g, h, s, p] such that f = Dg + h + s + p, h has a squarefree denominator normal w.r.t. D, and all the squarefree factors of the denominator of s are special w.r.t. D. Furthermore, h and s have no polynomial parts. D is the derivation to use on UP.

HermiteIntegrate: (Fraction UP, UP -> UP, UP) -> Record(answer: Fraction UP, logpart: Fraction UP, specpart: Fraction UP, polypart: UP)

HermiteIntegrate(f, D, d0) returns [g, h, s, p] such that f = Dg + g*d0 + h + s + p, h has a squarefree denominator normal w.r.t. D, and all the squarefree factors of the denominator of s are special w.r.t. D. Furthermore, h and s have no polynomial parts. D is the derivation to use on UP.