Struct SymmetryProfile 

pub struct SymmetryProfile {

    pub order: u128,
    pub generators: usize,
    pub num_orbits: usize,
    pub rank: usize,
    pub transitivity: usize,
    pub primitive: bool,
    pub blocks: Option<usize>,
    pub abelian: bool,
    pub solvable: Option<bool>,
    pub nilpotent: Option<bool>,
    pub derived_length: Option<usize>,
    pub nilpotency_class: Option<usize>,
    pub derived_order: u128,
    pub conjugacy_classes: Option<usize>,
    pub center_order: Option<u128>,
    pub exponent: Option<u128>,
    pub assignment_orbits: Option<u128>,
    pub abelianization: Option<(u128, u128)>,
    pub subgroups: Option<usize>,
    pub simple: Option<bool>,
    pub composition_factors: Option<Vec<u128>>,
    pub sylow: Option<Vec<(u128, usize)>>,
    pub real_classes: Option<usize>,
    pub rational_classes: Option<usize>,
    pub irreducible_degrees: Option<Vec<u128>>,
    pub frobenius_schur: Option<Vec<i8>>,
    pub isotypic_multiplicities: Option<Vec<u128>>,
    pub automorphism_order: Option<u128>,
    pub outer_automorphism_order: Option<u128>,
    pub coherent_rank: Option<usize>,
}

The structural profile of a formula’s variable-symmetry group — |Aut|, the orbit/rank/transitivity ladder, primitivity, and block structure. The data a surfacing layer (e.g. a Studio panel) needs to explain why an instance is symmetric.

Fields

order: u128

|Aut| of the phase-free variable-symmetry group (1 when there is no symmetry).

generators: usize

Number of detected generators.

num_orbits: usize

Variable orbits (points moved together).

rank: usize

Rank — orbits on ordered pairs (2 iff 2-transitive); 0 when not computed (group too large).

transitivity: usize

Transitivity degree, capped (1 = transitive, 2 = 2-transitive, …).

primitive: bool

Whether the (transitive) group is primitive.

blocks: Option<usize>

The number of minimal blocks when the group is transitive and imprimitive, else None.

abelian: bool

Whether the group is abelian.

solvable: Option<bool>

Whether the group is solvable (its derived series reaches the trivial group); None when not computed (group too large for the derived-series walk).

nilpotent: Option<bool>

Whether the group is nilpotent (its lower central series reaches the trivial group); strictly stronger than solvable. None when not computed.

derived_length: Option<usize>

Derived length (solvability class) — the depth of the derived series; None if unsolvable / not computed.

nilpotency_class: Option<usize>

Nilpotency class — the depth of the lower central series; None if not nilpotent / not computed.

derived_order: u128

Order of the derived (commutator) subgroup [G, G]; 0 when not computed.

conjugacy_classes: Option<usize>

Number of conjugacy classes (= number of irreducible representations); None when the group is too large to enumerate.

center_order: Option<u128>

Order of the centre Z(G); None when too large to enumerate.

exponent: Option<u128>

The exponent — lcm of element orders (smallest e with gᵉ = id for all g); None when too large to enumerate.

assignment_orbits: Option<u128>

The number of distinct {0,1} assignments to the variables up to symmetry (Pólya with 2 colours) — the symmetry-reduced size of the search space; None when too large to enumerate.

abelianization: Option<(u128, u128)>

The abelianisation G/[G,G] as (order, exponent) — the largest abelian quotient; None when too large to enumerate.

subgroups: Option<usize>

The number of subgroups (size of the subgroup lattice); None for larger groups (the lattice walk is gated more tightly than the other invariants).

simple: Option<bool>

Whether the group is simple (non-trivial, no normal subgroup but itself and {id}); None when too large to enumerate.

composition_factors: Option<Vec<u128>>

The composition factors (Jordan–Hölder) as the sorted multiset of their orders; their product is |G|. None when the lattice walk is out of range.

sylow: Option<Vec<(u128, usize)>>

The Sylow structure as (p, n_p) pairs — the number of Sylow p-subgroups per prime; None when the lattice walk is out of range.

real_classes: Option<usize>

The number of real conjugacy classes (= number of real irreducible characters); None when too large to enumerate.

rational_classes: Option<usize>

The number of rational conjugacy classes (= number of rational-valued irreducible characters) — the singleton Galois orbits. Strictly refines Self::real_classes (rational ≤ real); they differ exactly when a character is real but irrational. None when too large to enumerate.

irreducible_degrees: Option<Vec<u128>>

The irreducible-representation degrees χ_s(1) (sorted, Σ dᵢ² = |G|) from the Burnside–Dixon character table — the complete representation-theoretic fingerprint of the symmetry; None when the character table is out of range.

frobenius_schur: Option<Vec<i8>>

The Frobenius–Schur indicators (one per irreducible, aligned with the character table): +1 real, 0 complex, −1 quaternionic. Refines Self::real_classes and separates groups with identical character tables (D₄ vs Q₈). None when the character table is out of range.

isotypic_multiplicities: Option<Vec<u128>>

The isotypic decomposition of the variable-permutation representation: the multiplicity m_s of each irreducible in π = Σ_s m_s χ_s (aligned with the character table). Bridges the action and the linear theory — m_trivial = num_orbits, Σ m_s² = rank, Σ m_s·d_s = num_vars. None when out of range.

automorphism_order: Option<u128>

The order of Aut(G) — the automorphism group of the symmetry group itself. The intrinsic symmetry of G as an abstract group. None when out of range. Separates groups indistinguishable by character table / Frobenius–Schur / rationality (e.g. |Aut(D₄)|=8 vs |Aut(Q₈)|=24).

outer_automorphism_order: Option<u128>

The order of Out(G) = Aut(G)/Inn(G) — the outer automorphisms (those not realised by conjugation). None when out of range.

coherent_rank: Option<usize>

The coherent (association-scheme) rank — the number of relations in the coherent configuration that 2-WL stabilizes to (= two_wl_pair_cells), the combinatorial analog of the orbital rank. It is ≤ rank (2-WL can only be coarser than the true orbitals), so a value below rank witnesses that the polynomial pre-filter cannot resolve the full pair structure. Clause-derived: Some only from symmetry_structure (None for the pseudo-Boolean coefficient profile, which has no clauses).

Trait Implementations

impl Clone for SymmetryProfile

fn clone(&self) -> SymmetryProfile

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SymmetryProfile

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

Formats the value using the given formatter.

impl PartialEq for SymmetryProfile

fn eq(&self, other: &SymmetryProfile) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Eq for SymmetryProfile

impl StructuralPartialEq for SymmetryProfile