IntegrationResultRFToFunction R

irexpand.spad line 262 [edit on github]

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. Date Created: 21 August 1988

complexExpand: IntegrationResult Fraction Polynomial R -> Expression R

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

complexIntegrate: (Fraction Polynomial R, Symbol) -> Expression R if R has CharacteristicZero

complexIntegrate(f, x) returns the integral of f(x)dx where x is viewed as a complex variable.

expand: (IntegrationResult Fraction Polynomial R, Symbol) -> List Expression R

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

integrate: (Fraction Polynomial R, Symbol) -> Union(Expression R, List Expression R) if R has CharacteristicZero

integrate(f, x) returns the integral of f(x)dx where x is viewed as a real variable.

split: IntegrationResult Fraction Polynomial R -> IntegrationResult Fraction Polynomial R

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.