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

In this article, we will make a NumPy program to multiply one polynomial to another. Two polynomials are given as input and the result is the multiplication of two polynomials.

• 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 q(x) then multiply these to get r(x) = p(x) * q(x) as a result of multiplication of two input polynomials.

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

then result is r(x) = p(x) * q(x) 

and output is 

( (A1 * B1), (A2 * B1) + (A2 * B1),
(A3 * B1) + (A2 * B2) + (A1 * B3), 
(A2 * B2) + (A3 * B2), (A3 * B3) ).

This can be calculated using the polymul() method of NumPy. This method evaluates the product of two polynomials and returns the polynomial resulting from the multiplication of two input polynomials ‘p1’ and ‘p2’.

Syntax:

numpy.polymul(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)
# q(x) = 2(x**2) + (-5)x +2
qx = (2, -5, 2)

# mul the polynomials
rx = numpy.polynomial.polynomial.polymul(px, qx)

# print the resultant polynomial
print(rx)

Output :

[ 10. -29.  30. -29.  10.] 

Example 2 :

Python3

# importing package
import numpy

# define the polynomials
# p(x) = 2.2
px = (0, 0, 2.2)

# q(x) = 9.8(x**2) + 4
qx = (9.8, 0, 4)

# mul the polynomials
rx = numpy.polynomial.polynomial.polymul(px, qx)

# print the resultant polynomial
print(rx)

Output :

[  0.     0.    21.56   0.     8.8 ]

Example 3 :

Python3

# importing package
import numpy

# define the polynomials
# p(x) = (5/3)x
px = (0, 5/3, 0)

# q(x) = (-7/4)(x**2) + (9/5)
qx = (-7/4, 0, 9/5)

# mul the polynomials
rx = numpy.polynomial.polynomial.polymul(px, qx)

# print the resultant polynomial
print(rx)

Output :

[ 0.         -2.91666667  0.          3.        ]