ApartSquareFree

rewrites a rational expression as a sum of terms whose denominators are powers of square-free polynomials.

treats all variables other than var as constants.

Details and Options

ApartSquareFree gives the square-free partial fraction decomposition of a rational expression.
ApartSquareFree[expr,Trig->True] treats trigonometric functions as rational functions of exponentials, and manipulates them accordingly.
ApartSquareFree automatically threads over lists in expr, as well as equations, inequalities, and logic functions.

Examples

open all close all

Decompose into partial fractions using square-free factorization of the denominator:

Decompose into partial fractions using full factorization of the denominator:

Decompose a rational function into partial fractions using square-free factorization:

ApartSquareFree can handle symbolic parameters:

Treat as the main variable and as a constant:

Here ApartSquareFree picks as the main variable and treats as a constant:

ApartSquareFree can handle non-polynomial expressions:

ApartSquareFree threads over equations and inequalities:

Compute the square-free partial fraction representation over the integers modulo :

Compute the square-free partial fraction representation following common trigonometric identities:

Partial fraction decomposition over the rationals:

Partial fraction decomposition over the integers modulo 2:

Partial fraction decomposition of a trigonometric expression:

Together acts as an inverse of ApartSquareFree:

Top