Partial fractions

Partial fraction expansion is used to change a rational fraction in the form fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction, where f and g are polynomials, into an expression of the form sum for j of fraction numerator f subscript j left parenthesis x right parenthesis over denominator g subscript j left parenthesis x right parenthesis end fraction, where g subscript j left parenthesis x right parenthesis are polynomials that are factors of g left parenthesis x right parenthesis.

partial_fractions(Fraction)

Given a fraction of polynomials, returns a list L whose elements are lists L subscript 1, ..., L subscript k. The list L subscript j has as elements the polynomials f subscript j left parenthesis x right parenthesis and g subscript j left parenthesis x right parenthesis.

partial_fractions(Fraction, Ring)

Given a fraction of polynomials and a ring, returns a list L whose elements are lists L subscript 1, ..., L subscript k. The list L subscript j has as elements the polynomials f subscript j left parenthesis x right parenthesis and g subscript j left parenthesis x right parenthesis. The decomposition is done over the specified ring.