ApartSquareFree

✖
`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

open allclose all

Basic Examples (1)Summary of the most common use cases

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

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-iksga

Out[1]=1

Decompose into partial fractions using full factorization of the denominator:

In[2]:=2

✖

https://wolfram.com/xid/0e5bndthawvcfa-zlr7z

Out[2]=2

Scope (7)Survey of the scope of standard use cases

Basic Uses (5)

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

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-0o87vt

Out[1]=1

ApartSquareFree can handle symbolic parameters:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-w0j56z

Out[1]=1

Treat as the main variable and as a constant:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-wq65oj

Out[1]=1

Treat as the main variable and as a constant:

In[2]:=2

✖

https://wolfram.com/xid/0e5bndthawvcfa-r893af

Out[2]=2

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

In[3]:=3

✖

https://wolfram.com/xid/0e5bndthawvcfa-mrqn1a

Out[3]=3

ApartSquareFree can handle non-polynomial expressions:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-tu5h9

Out[1]=1

ApartSquareFree threads over equations and inequalities:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-xgrdv8

Out[1]=1

Advanced Uses (2)

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

In[13]:=13

✖

https://wolfram.com/xid/0e5bndthawvcfa-qjg6q7

Out[13]=13

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

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-qdlqle

Out[1]=1

Options (2)Common values & functionality for each option

Modulus (1)

Partial fraction decomposition over the rationals:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-mezan7

Out[1]=1

Partial fraction decomposition over the integers modulo 2:

In[2]:=2

✖

https://wolfram.com/xid/0e5bndthawvcfa-gf138f

Out[2]=2

Trig (1)

Partial fraction decomposition of a trigonometric expression:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-vzydk

Out[1]=1

Properties & Relations (1)Properties of the function, and connections to other functions

Together acts as an inverse of ApartSquareFree:

In[1]:=1

✖

https://wolfram.com/xid/0e5bndthawvcfa-d0y721

Out[1]=1

In[2]:=2

✖

https://wolfram.com/xid/0e5bndthawvcfa-crfkbf

Out[2]=2

Top