Struct SolutionSpace 

pub struct SolutionSpace {
    pub num_vars: usize,
    pub particular: Vec<bool>,
    pub kernel_basis: Vec<Vec<bool>>,
}

The complete solution space of a GF(2) linear system A x = b, in symmetry-broken form: one particular solution x₀ plus a basis of the kernel. Every solution is x₀ ⊕ (a GF(2) combination of the kernel basis), so the entire affine coset — all 2^{n−rank} solutions — is generated from this compressed witness. The kernel is the symmetry group of the solution set (the translations that preserve Ax), x₀ is one witness, and the basis are its generators: this is the exact, polynomial, linear analog of hypercube::model_orbit. The harder the break (the bigger the kernel), the more solutions; an invertible system has a trivial kernel — no symmetry, a unique witness.

Fields

num_vars: usize

particular: Vec<bool>

kernel_basis: Vec<Vec<bool>>

Implementations

impl SolutionSpace

pub fn count(&self) -> u128

The number of solutions: 2^{dim kernel} (rank–nullity) — the orbit size of the solution coset.

pub fn enumerate(&self) -> Vec<Vec<bool>>

Generate every solution by XORing the particular solution with each subset of the kernel basis — the orbit of x₀ under the kernel’s translation symmetry.

Trait Implementations

impl Clone for SolutionSpace

fn clone(&self) -> SolutionSpace

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SolutionSpace

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

Formats the value using the given formatter.

impl PartialEq for SolutionSpace

fn eq(&self, other: &SolutionSpace) -> 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 SolutionSpace

impl StructuralPartialEq for SolutionSpace