ApartSquareFree

ApartSquareFree[expr]

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

ApartSquareFree[expr,var]

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

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Basic Examples  (1)

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

Decompose into partial fractions using full factorization of the denominator:

Scope  (3)

ApartSquareFree can handle symbolic parameters:

Treat x as the main variable and y as a constant:

Treat y as the main variable and x as a constant:

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

ApartSquareFree threads over equations and inequalities:

Options  (2)

Modulus  (1)

Partial fraction decomposition over the rationals:

Partial fraction decomposition over the integers modulo 2:

Trig  (1)

Partial fraction decomposition of a trigonometric expression:

Properties & Relations  (1)

Together acts as an inverse of ApartSquareFree:

Introduced in 2007
 (6.0)