# IntegrationResultRFToFunction R¶

irexpand.spad line 222 [edit on github]

R: Join(GcdDomain, RetractableTo Integer, Comparable, LinearlyExplicitOver Integer)

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`

.