Function factor_multivariate 

pub fn factor_multivariate<O: MonomialOrd>(
    f: &MultiPoly<O>,
) -> Option<MultiFactorization<O>>

Factor a multivariate polynomial over ℤ by Kronecker substitution.

Returns Some((content, factors)) with f = content · ∏ gᵢ^mᵢ, every gᵢ a primitive integer polynomial with positive leading coefficient (in the monomial order O), sorted for determinism. Returns None if the polynomial is too large for the method (see MAX_KRONECKER_SUBSTITUTION_DEGREE) or if the result could not be verified — a result is never returned without being multiplied back.

Algorithm

1. Remove rational and monomial content.
2. If only one variable remains, factor with factor_zassenhaus.
3. Otherwise substitute xⱼ → t^{Dⱼ} with mixed radices Dⱼ₊₁ = Dⱼ · (deg_{xⱼ} f + 1), which is injective on the monomials of f, factor the univariate image, and regroup its irreducible factors (with multiplicity) into subsets whose products map back to genuine divisors of f (checked by exact multivariate division). All variable orderings are tried, cheapest first.

Examples

use symplex::factor_zassenhaus::factor_multivariate;
use symplex::multipoly::MultiPoly;

let [x, y]: [MultiPoly; 2] = [MultiPoly::var(2, 0), MultiPoly::var(2, 1)];
// x³ − y³ = (x − y)(x² + xy + y²)
let f = x.mul(&x).mul(&x).sub(&y.mul(&y).mul(&y));
let (content, factors) = factor_multivariate(&f).unwrap();
assert!(content.is_integer());
assert_eq!(factors.len(), 2);
let mut back = MultiPoly::constant(2, content);
for (g, m) in &factors {
    for _ in 0..*m { back = back.mul(g); }
}
assert_eq!(back, f);