Struct Bsgs 

pub struct Bsgs {
    pub degree: usize,
    pub base: Vec<usize>,
    /* private fields */
}

A base and strong generating set, with the per-level basic transversals.

Fields

degree: usize

base: Vec<usize>

Implementations

impl Bsgs

pub fn order(&self) -> u128

|G| = Π |Δᵢ| — exact for |G| up to the u128 range (any degree below ~33 factorial).

pub fn elements(&self, cap: usize) -> Option<Vec<Perm>>

Enumerate all |G| group elements, as the unique products u_k·…·u₂·u₁ of one transversal element per level. (sift divides g by the level-i transversal element on the right, so g = h·u₁ with h ∈ G⁽²⁾, recursing to g = u_k·…·u₁ — deepest level innermost; we accumulate from the deepest level outward.) Returns None if |G| > cap — the BSGS knows the order without enumerating, so the caller gates on it. The basis of complete symmetry breaking.

pub fn transversal_elements(&self) -> Vec<Perm>

All coset representatives across the stabilizer chain — the transversal elements at every level. There are Σ |Δᵢ| of them (polynomial: at most degree²), spread across the group, so a lex-leader symmetry break over them (together with the generators) is stronger than the bare generators yet still polynomial, unlike the complete enumeration (|G|). This is the stabilizer chain breaking the symmetry level by level — “symmetry break again” at each base point.

pub fn contains(&self, g: &[usize]) -> bool

Is g a member of the group (i.e., does it sift to the identity through the chain)? This is the coset decision: g ∈ rep·G iff rep⁻¹·g is a member.

Trait Implementations

impl Clone for Bsgs

fn clone(&self) -> Bsgs

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Bsgs

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

Formats the value using the given formatter.