# Polynomial Multiplication in Python

In this tutorial, we are going to learn how to multiply two polynomials in Python.

## Polynomial Multiplication

Let’s consider two polynomials P, Q. Where P is 2+3x^1+4x^3 and Q is 1+2x^1+4x^2+5x^3. The product of the polynomials P and Q is 2+7x^1+14x^2+26x^3+23x^4+16x^5+20x^6.

The product of two polynomials is the multiplication of every term of the first polynomial with every term in the second polynomial. For instance, let’s the length of the polynomial P, Q is m, n respectively.

**Approach**

1) Firstly create a result array of size m+n-1 which stores the result.

2) Secondly, initialize all the values in result[] to 0.

3) Multiply every element in polynomial P with every element in polynomial Q

result[i+j] = result[i+j]+P[i]*Q[j]

4) return the result

def polynomial_multiplication(P, Q): m = len(P) n = len(Q) result = [0]*(m+n-1) for i in range(m): for j in range(n): result[i+j] += P[i]*Q[j] return result # function that print polynomial def polynomial(poly): n = len(poly) for i in range(n): print(poly[i], end = "") if (i != 0): print("x^", i, end = "") if (i != n - 1): print(" + ", end = "") # polynomial in array representation P = [2, 3, 0, 4] print("First polynomial is:") polynomial(P) print('\n') Q = [1, 2, 4, 5] print("Second polynomial is: ") polynomial(Q) print('\n') result = (polynomial_multiplication(P, Q)) print("Product of polynomials is: ") polynomial(result)

Output

First polynomial is: 2 + 3x^ 1 + 0x^ 2 + 4x^ 3 Second polynomial is: 1 + 2x^ 1 + 4x^ 2 + 5x^ 3 Product of polynomials is: 2 + 7x^ 1 + 14x^ 2 + 26x^ 3 + 23x^ 4 + 16x^ 5 + 20x^ 6

Also, read

–Hi

Can you get rid of the space between “^” and the degree that follows it?

For example: “x^3” instead of “x^ 3”

Thanks.

–Sam

def poly_str(arr):

“”” string representation of polynomial.

arr are the coefficients from high to low order.

“””

n = len(arr)

res = “”

for i in range(n):

v = arr[i]

# catch the leading negative sign

if i == 0:

if v < 0:

res = "-"

else:

# separating sign

if v < 0:

res += " – "

else:

res += " + "

p = n-i-1

if p == 0:

# constant term

res += f"{abs(v)}"

elif p == 1:

# x term

if v == 1:

res += f"x"

else:

res += f"{abs(v)} x"

else:

# other x ** p terms

if v == 1:

res += f"x**{p}"

else:

res += f"{abs(v)} x**{p}"

return res