Python Program to Compute a Polynomial Equation given that the Coefficients of the Polynomial are stored in a List

When you need to compute a polynomial equation where the coefficients are stored in a list, you can use nested loops to calculate each term. A polynomial like 2x³ + 5x² + 3x + 0 can be evaluated by multiplying each coefficient by the corresponding power of x.

Understanding Polynomial Evaluation

For a polynomial represented as a list [2, 5, 3, 0], this corresponds to:

• 2x³ (coefficient 2, power 3)

• 5x² (coefficient 5, power 2)

• 3x¹ (coefficient 3, power 1)

• 0x? (coefficient 0, power 0)

Example

Here's how to evaluate the polynomial when x = 2 ?

coefficients = [2, 5, 3, 0]
x = 2
poly_len = len(coefficients)
result = 0

for i in range(poly_len):
    term = coefficients[i]
    for j in range(poly_len - i - 1):
        term = term * x
    result = result + term

print("The polynomial equation for the given list of coefficients is:")
print(result)

The polynomial equation for the given list of coefficients is:
42

How It Works

The algorithm works by calculating each term of the polynomial:

• Term 1: 2 × 2³ = 2 × 8 = 16

• Term 2: 5 × 2² = 5 × 4 = 20

• Term 3: 3 × 2¹ = 3 × 2 = 6

• Term 4: 0 × 2? = 0 × 1 = 0

Final result: 16 + 20 + 6 + 0 = 42

Alternative Method Using Built-in Power Function

You can also use Python's pow() function for cleaner code ?

coefficients = [2, 5, 3, 0]
x = 2
result = 0

for i, coeff in enumerate(coefficients):
    power = len(coefficients) - i - 1
    result += coeff * pow(x, power)

print("Polynomial result:", result)

Polynomial result: 42

Conclusion

To evaluate a polynomial from a coefficient list, multiply each coefficient by the variable raised to the appropriate power. The nested loop approach builds powers by repeated multiplication, while using pow() provides a more direct solution.