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.