Subtract one polynomial to another in Python

To subtract one polynomial from another in Python, use the numpy.polynomial.polynomial.polysub() method. This function returns the difference 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*x².

The method returns a coefficient array representing their difference. The parameters c1 and c2 are 1-D arrays of polynomial coefficients ordered from low to high.

Syntax

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

Parameters

c1, c2: 1-D arrays of polynomial coefficients ordered from low to high degree.

Example

Let's subtract two polynomials using polysub() ?

from numpy.polynomial import polynomial as P

# Define two polynomials
# p1 represents: 3 + 1*x + 6*x²
# p2 represents: 2 + 7*x + 3*x²
p1 = (3, 1, 6)
p2 = (2, 7, 3)

# Display the polynomials
print("Polynomial 1:", p1)
print("Polynomial 2:", p2)

# Subtract p2 from p1
result = P.polysub(p1, p2)
print("Result (p1 - p2):", result)

Polynomial 1: (3, 1, 6)
Polynomial 2: (2, 7, 3)
Result (p1 - p2): [ 1. -6.  3.]

How It Works

The subtraction is performed coefficient-wise:

• Constant term: 3 - 2 = 1
• x coefficient: 1 - 7 = -6
• x² coefficient: 6 - 3 = 3

So the result represents: 1 - 6*x + 3*x²

Different Length Polynomials

The method handles polynomials of different degrees automatically ?

from numpy.polynomial import polynomial as P

# Different degree polynomials
p1 = (1, 2, 3, 4)    # 1 + 2*x + 3*x² + 4*x³
p2 = (5, 6)          # 5 + 6*x

result = P.polysub(p1, p2)
print("Result:", result)
print("Represents: -4 - 4*x + 3*x² + 4*x³")

Result: [-4. -4.  3.  4.]
Represents: -4 - 4*x + 3*x² + 4*x³

Conclusion

Use numpy.polynomial.polynomial.polysub() to subtract polynomials coefficient-wise. The function automatically handles polynomials of different degrees and returns the result as a NumPy array.