Function winter_math::polynom::syn_div

pub fn syn_div<E>(p: &[E], a: usize, b: E) -> Vec<E>
where
    E: FieldElement,

Returns a polynomial resulting from dividing a polynomial by a polynomial of special form.

Specifically, divides polynomial p by polynomial (x^a - b) using synthetic division method; if the polynomials don’t divide evenly, the remainder is ignored. Polynomial p is expected to be in the coefficient form, and the result will be in the coefficient form as well. The length of the resulting polynomial will be equal to p.len().

This function is significantly faster than the generic polynom::div() function.

Panics

Panics if:

• a is zero;
• b is zero;
• p.len() is smaller than or equal to a.

Examples

// p(x) = x^3 + x^2 + 2 * x + 2
let p = [
    BaseElement::new(2),
    BaseElement::new(2),
    BaseElement::new(1),
    BaseElement::new(1),
];

// expected result = x^2 + 2
let expected = vec![
    BaseElement::new(2),
    BaseElement::ZERO,
    BaseElement::new(1),
    BaseElement::ZERO,
];

// divide by x + 1
assert_eq!(expected, syn_div(&p, 1, -BaseElement::ONE));