Struct PolynomialSystem 

pub struct PolynomialSystem {
    pub polys: Vec<String>,
    pub vars: Vec<String>,
}

Polynomial system: a system of polynomial equations.

Fields

polys: Vec<String>

The polynomial generators (as strings).

vars: Vec<String>

Variable names.

Implementations

impl PolynomialSystem

pub fn new(polys: Vec<String>, vars: Vec<String>) -> Self

Create a new polynomial system.

pub fn solve_over_algebraic_closure(&self) -> Vec<String>

Solve over the algebraic closure using Gröbner bases.

Computes the variety V(f_1,…,f_m) ⊆ k̄^n via the Shape Lemma: for 0-dimensional ideals, the reduced Gröbner basis in lex order gives a triangular system solvable by back-substitution.

pub fn count_solutions(&self) -> usize

Count solutions (degree of the ideal) for 0-dimensional systems.

By Bézout’s theorem, the number of solutions (counted with multiplicity) equals the product of degrees of the generators (for generic systems).