How to divide a polynomial to another using NumPy in Python?

In this article, we will make a NumPy program to divide one polynomial to another. Two polynomials are given as input and the result is the quotient and remainder of the division.

• The polynomial p(x) = C3 x2 + C2 x + C1  is represented in NumPy as : ( C1, C2, C3 ) { the coefficients (constants)}.
• Let take two polynomials p(x) and g(x) then divide these to get quotient q(x) = p(x) // g(x) and  remainder r(x) = p(x) % g(x) as a result.

If p(x) = A3 x2 + A2 x + A1
and 
g(x) = B3 x2 + B2 x + B1 

then result is 
q(x) = p(x) // g(x) and r(x) = p(x) % g(x)

and the output is coefficients of remainder and
 the coefficients of quotient.

This can be calculated using the polydiv() method. This method evaluates the division of two polynomials and returns the quotient and remainder of the polynomial division.

Syntax:

numpy.polydiv(p1, p2)

Below is the implementation with some examples :

Example 1 :  

Python3

# importing package
import numpy

# define the polynomials
# p(x) = 5(x**2) + (-2)x +5
px = (5, -2, 5)

# g(x) = x +2
gx = (2, 1, 0)

# divide the polynomials
qx, rx = numpy.polynomial.polynomial.polydiv(px, gx)

# print the result
#quotient
print(qx)

# remainder
print(rx)

Output :

[-12.   5.]
[ 29.]

Example 2 : 

Python3

# importing package
import numpy

# define the polynomials
# p(x) = (x**2) + 3x + 2
px = (1,3,2)

# g(x) = x + 1
gx = (1,1,0)

# divide the polynomials
qx,rx = numpy.polynomial.polynomial.polydiv(px,gx)

# print the result
# quotient
print(qx)

# remainder
print(rx)

Output :

[ 1.  2.]
[ 0.]