Add one polynomial to another in Python

To add one polynomial to another in Python, use the numpy.polynomial.polynomial.polyadd() method. This function returns the sum of two polynomials c1 + c2. The arguments are sequences of coefficients from lowest order term to highest, i.e., [1,2,3] represents the polynomial 1 + 2*x + 3*x**2.

The numpy.polynomial.polynomial module provides a number of objects useful for dealing with polynomials, including a Polynomial class that encapsulates the usual arithmetic operations.

Syntax

numpy.polynomial.polynomial.polyadd(c1, c2)

Parameters

The method takes the following parameters ?

• c1, c2 ? 1-D arrays of polynomial coefficients ordered from low to high

Return Value

Returns a 1-D array representing the coefficient array of their sum.

Example

Let's see how to add two polynomials using polyadd() method ?

from numpy.polynomial import polynomial as P

# Declare two polynomials
# p1 represents: 4 + 1*x + 6*x^2
# p2 represents: 2 + 5*x + 3*x^2
p1 = (4, 1, 6)
p2 = (2, 5, 3)

# Display the polynomials
print("Polynomial 1...\n", p1)
print("\nPolynomial 2...\n", p2)

# Add the polynomials
sum_result = P.polyadd(p1, p2)
print("\nResult (Sum)...\n", sum_result)

Polynomial 1...
(4, 1, 6)

Polynomial 2...
(2, 5, 3)

Result (Sum)...
[6. 6. 9.]

How It Works

The addition works coefficient-wise ?

• Constant term: 4 + 2 = 6
• x coefficient: 1 + 5 = 6
• x² coefficient: 6 + 3 = 9

So (4 + 1*x + 6*x²) + (2 + 5*x + 3*x²) = 6 + 6*x + 9*x²

Adding Polynomials of Different Degrees

The method handles polynomials of different degrees automatically ?

from numpy.polynomial import polynomial as P

# Different degree polynomials
p1 = (1, 2)        # 1 + 2*x
p2 = (3, 4, 5)     # 3 + 4*x + 5*x^2

result = P.polyadd(p1, p2)
print("Sum of different degree polynomials:", result)

Sum of different degree polynomials: [4. 6. 5.]

Conclusion

The numpy.polynomial.polynomial.polyadd() method provides an efficient way to add polynomials by summing their coefficients element-wise. It automatically handles polynomials of different degrees and returns the result as a NumPy array.