Python | sympy.apart() method
Last Updated :
25 Jun, 2019
With the help of sympy.apart() method, we can performs a partial fraction decomposition on a rational mathematical expression.
Syntax: apart(expression)
Parameters:
expression – It is a rational mathematical expression.
Returns: Returns an expression after the partial decomposition.
Example #1:
In this example we can see that by using sympy.apart() method, we can get a partial fraction decomposition of a given mathematical expression.
from sympy import *
x = symbols( 'x' )
expr = ( 4 * x * * 3 + 21 * x * * 2 + 10 * x + 12 ) / (x * * 4 + 5 * x * * 3 + 5 * x * * 2 + 4 * x)
print ( "Mathematical expression : {}" . format (expr))
pd = apart(expr)
print ( "After Partial Decomposition : {}" . format (pd))
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Output:
Mathematical expression : (4*x**3 + 21*x**2 + 10*x + 12)/(x**4 + 5*x**3 + 5*x**2 + 4*x)
After Partial Decomposition : (2*x - 1)/(x**2 + x + 1) - 1/(x + 4) + 3/x
Example #2:
from sympy import *
x = symbols( 'x' )
expr = 1 / (x + 3 )(x + 2 )
print ( "Mathematical expression : {}" . format (expr))
pd = apart(expr)
print ( "After Partial Decomposition : {}" . format (pd))
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Output:
Mathematical expression : 1/((x + 2)*(x + 3))
After Partial Decomposition : -1/(x + 3) + 1/(x + 2)
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