Struct TropicalGroebnerComputer 

pub struct TropicalGroebnerComputer {
    pub weight: Vec<f64>,
    pub generators: Vec<Polynomial>,
    pub nvars: usize,
}

A tropical Gröbner basis computation for a weighted ideal.

Given an ideal I ⊆ k[x_1,…,x_n] and a weight vector w ∈ R^n, the initial ideal in_w(I) is generated by {in_w(f) : f ∈ I}. The tropical variety Trop(I) = {w : in_w(I) contains no monomial}.

Fields

weight: Vec<f64>

The weight vector w.

generators: Vec<Polynomial>

The ideal generators.

nvars: usize

Number of variables.

Implementations

impl TropicalGroebnerComputer

pub fn new(weight: Vec<f64>, generators: Vec<Polynomial>, nvars: usize) -> Self

Create a new tropical Gröbner computer.

pub fn weighted_degree(&self, m: &Monomial) -> f64

Compute the weighted degree of a monomial m w.r.t. w: w(m) = ∑_i w_i · m_i.

pub fn initial_form(&self, f: &Polynomial) -> Polynomial

Compute the initial form in_w(f): keep only terms achieving the maximum weighted degree.

pub fn is_in_tropical_variety(&self) -> bool

Check if the weight vector w is in the tropical variety of the ideal (heuristic: check if no initial form of any generator is a monomial).

pub fn tropical_monomial_count(&self) -> usize

Compute the tropical degree: number of generators whose initial form is a monomial.