Python | sympy.apart() method

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.

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# import sympy
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))
    
# Use sympy.apart() method
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:

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# import sympy
from sympy import * 
  
x = symbols('x')
expr = 1/(x + 3)(x + 2)
  
print("Mathematical expression : {}".format(expr))
    
# Use sympy.factor_list() method
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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