IntegrationResultToFunction(R, F)

irexpand.spad line 1 [edit on github]

• R : Join(GcdDomain, RetractableTo(Integer), Comparable, LinearlyExplicitOver(Integer))
• F : Join(AlgebraicallyClosedFunctionSpace(R), TranscendentalFunctionCategory)

This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents, provided that the indexing polynomial can be factored into quadratics.

complexExpand : IntegrationResult(F) -> F

complexExpand(i) returns the expanded complex function corresponding to i.

expand : (IntegrationResult(F), Symbol) -> List(F)

expand(i, x) returns the list of possible real functions of x corresponding to i.

split : IntegrationResult(F) -> IntegrationResult(F)

split(u(x) + sum_P(a)=0 Q(a, x)) returns u(x) + sum_P1(a)=0 Q(a, x) + ... + sum_Pn(a)=0 Q(a, x) where P1, ..., Pn are the factors of P.