Struct HilbertFunction 

pub struct HilbertFunction {
    pub values: Vec<usize>,
}

Hilbert function H(I, t) = dim_k(R/I)_t for a homogeneous ideal I.

Fields

values: Vec<usize>

Precomputed values: H(I, 0), H(I, 1), …, H(I, max_degree).

Implementations

impl HilbertFunction

pub fn compute(rgb: &ReducedGroebnerBasis, max_degree: usize) -> Self

Compute the Hilbert function from a reduced Gröbner basis.

Uses the combinatorial formula: H(I, t) = #{monomials of degree t} − #{standard monomials of degree t in LT(I)}.

pub fn at(&self, t: usize) -> usize

Retrieve H(I, t).

pub fn euler_characteristic(&self) -> i64

Compute the Euler characteristic ∑_t (-1)^t H(I, t) (truncated to stored values).

Trait Implementations

impl Clone for HilbertFunction

fn clone(&self) -> HilbertFunction

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for HilbertFunction

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.