IntegrationResultRFToFunction(R)

irexpand.spad line 262 [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.