Module winter_math::polynom

Basic polynomial operations.

This module provides a set of function for basic polynomial operations, including:

• Polynomial evaluation using Horner method.
• Polynomial interpolation using Lagrange method.
• Polynomial addition, subtraction, multiplication, and division.
• Synthetic polynomial division for efficient division by polynomials of the form x^a - b.

In the context of this module any slice of field elements is considered to be a polynomial in reverse coefficient form. A few examples:

// p(x) = 2 * x + 1
let p = vec![BaseElement::new(1), BaseElement::new(2)];

// p(x) = 4 * x^2 + 3
let p = [BaseElement::new(3), BaseElement::ZERO, BaseElement::new(4)];

Functions

• add
  Returns a polynomial resulting from adding two polynomials together.
• degree_of
  Returns the degree of the provided polynomial.
• div
  Returns a polynomial resulting from dividing one polynomial by another.
• eval
  Evaluates a polynomial at a single point and returns the result.
• eval_many
  Evaluates a polynomial at multiple points and returns a vector of results.
• interpolate
  Returns a polynomial in coefficient form interpolated from a set of X and Y coordinates.
• interpolate_batch
  Returns a vector of polynomials interpolated from the provided X and Y coordinate batches.
• mul
  Returns a polynomial resulting from multiplying two polynomials together.
• mul_by_scalar
  Returns a polynomial resulting from multiplying a given polynomial by a scalar value.
• poly_from_roots
  Returns the coefficients of polynomial given its roots.
• remove_leading_zeros
  Returns a polynomial with all leading ZERO coefficients removed.
• sub
  Returns a polynomial resulting from subtracting one polynomial from another.
• syn_div
  Returns a polynomial resulting from dividing a polynomial by a polynomial of special form.
• syn_div_in_place
  Divides a polynomial by a polynomial of special form and saves the result into the original polynomial.
• syn_div_roots_in_place
  Divides a polynomial by a polynomial given its roots and saves the result into the original polynomial.