sympy.integrals.rationaltools.ratint_ratpart() in python

With the help of ratint_ratpart() method, we can implement the Horowitz Ostrogradsky algorithm and it will return the fractions A and B by using this method.

Syntax : ratint_ratpart(f, g, x)

Return : Return the fraction A and B.

Example #1 :

In this example we can see that by using ratint_ratpart() method, we are able to compute the rational integration using Horowitz Ostrogradsky algorithm and return the fractions A and B.

Python3

# import ratint_ratpart
from sympy.integrals.rationaltools import ratint_ratpart
from sympy.abc import x, y
from sympy import Poly

# Using ratint_ratpart() method
gfg = ratint_ratpart(Poly(5, x, domain='ZZ'), Poly(x**4 + 1, x, domain='ZZ'), x)

print(gfg)

Output :

(0, 5/(x**4 + 1))

Example #2 :

Python3

# import ratint_ratpart
from sympy.integrals.rationaltools import ratint_ratpart
from sympy.abc import x, y
from sympy import Poly

# Using ratint_ratpart() method
gfg = ratint_ratpart(Poly(13, x, domain='ZZ'), Poly(4*x**2 + x - 2, x, domain='ZZ'), x)

print(gfg)

Output :

(0, 13/(4*x**2 + x – 2))