This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

ApartSquareFree

ApartSquareFree[expr]
rewrites a rational expression as a sum of terms whose denominators are powers of square-free polynomials.
ApartSquareFree
treats all variables other than var as constants.
  • 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.
Decompose into partial fractions using square-free factorization of the denominator:
Decompose into partial fractions using full factorization of the denominator:
Decompose into partial fractions using square-free factorization of the denominator:
In[1]:=
Click for copyable input
Out[1]=
Decompose into partial fractions using full factorization of the denominator:
In[2]:=
Click for copyable input
Out[2]=
ApartSquareFree can handle symbolic parameters:
Treat as the main variable and as a constant:
Treat as the main variable and as a constant:
Here ApartSquareFree picks as the main variable and treats as a constant:
ApartSquareFree threads over equations and inequalities:
Partial fraction decomposition over the rationals:
Partial fraction decomposition over the integers modulo 2:
Partial fraction decomposition of a trigonometric expression:
New in 6