Adds two polynomial field elements.

Checks if two elements are equal.

Computes the modular inverse using the extended Euclidean algorithm. Returns {:ok, inverse} or {:error, :not_invertible} if the element is zero.

Multiplies two polynomial field elements with modular reduction. This implementation uses an optimized multiplication algorithm.

Negates a polynomial field element.

Creates a polynomial extension field element from coefficients.

Returns the one element.

Subtracts two polynomial field elements.

Returns the zero element.

Checks if the element is zero.