sympy.integrals.rationaltools.ratint_logpart() in python

With the help of ratint_logpart() method, we can integrate the indefinite rational function by implementing Lazard Rioboo Trager algorithm by using this method and returns the integrated polynomial.

Syntax : ratint_logpart(f, g, x, t=None)

Return : Return the integrated function.

Example #1 :

In this example we can see that by using ratint_logpart() method, we are able to compute the indefinite rational integration using Lazard Rioboo Trager algorithm.

# import ratint_logpart
from sympy.integrals.rationaltools import ratint_logpart
from sympy.abc import x
from sympy import Poly

# Using ratint_logpart() method
gfg = ratint_logpart(Poly(1, x, domain='ZZ'), 
                     Poly(x*2 + x + 1, x, domain='ZZ'), x)

print(gfg)

Output :

[(Poly(3*x + 1, x, domain='ZZ'), Poly(-3*_t + 1, _t, domain='ZZ'))]

Example #2 :

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

# Using ratint_logpart() method
gfg = ratint_logpart(Poly(10, y, domain='ZZ'), 
               Poly(y**2 - 3*y - 2, y, domain='ZZ'), y)

print(gfg)

Output :

[(Poly(y - 17*_t/20 - 3/2, y, domain='QQ[_t]'), Poly(-17*_t**2 + 100, _t, domain='ZZ'))]