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.
# 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)) |
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:
# 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)) |
Output:
Mathematical expression : 1/((x + 2)*(x + 3)) After Partial Decomposition : -1/(x + 3) + 1/(x + 2)
