Struct ActionGroupoid 

pub struct ActionGroupoid { /* private fields */ }

The action groupoid X ⫽ G: assignments over nv variables acted on by the group generated by gens (literal permutations). Small nv only — it enumerates all 2^nv objects, which is the point: it makes the orbit collapse visible and checkable.

Implementations

impl ActionGroupoid

pub fn new(nv: usize, gens: Vec<Perm>) -> Self

pub fn orbits(&self) -> Vec<u32>

The orbit id of every assignment — π₀(X ⫽ G), computed as the connected components of the action via union-find. orbits()[a] is the canonical representative (smallest member) of a’s orbit.

pub fn num_orbits(&self) -> usize

|π₀(X ⫽ G)| — the number of essentially-different worlds, i.e. exactly what symmetry breaking reduces the search space to.

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

The full group G generated by gens (closed under composition, including the identity). Bounded to cap elements so a pathological generating set can’t blow up; the caller’s small examples are well within it.

pub fn stabilizer_size(&self, a: u32, group: &[Perm]) -> usize

π₁(X ⫽ G) at the assignment a — its stabilizer: the group elements that fix a (g · a = a). These are the loops at a in the action groupoid; the fundamental-group data of the homotopy type at that component.

pub fn orbit_size(&self, a: u32) -> usize

The size of a’s orbit (the connected component of a).