Struct PhaseSpace 

pub struct PhaseSpace {
    pub n: usize,
    pub mul: Vec<Vec<usize>>,
    pub identity: usize,
    pub bot: Vec<bool>,
}

A phase space: a commutative monoid (M, ·, e) with distinguished subset bot. We represent M as integers mod p for concreteness.

Fields

n: usize

Elements of the monoid (indices 0..n).

mul: Vec<Vec<usize>>

Multiplication table: mul[i][j] = i · j.

identity: usize

Identity element.

bot: Vec<bool>

The distinguished subset ⊥ ⊆ M.

Implementations

impl PhaseSpace

pub fn new(_name: &str) -> Self

Create a named trivial phase space {e} with ⊥ = {e}. The _name parameter is informational only.

pub fn completeness_description(&self) -> String

Description of completeness for phase semantics.

pub fn trivial() -> Self

Create the trivial phase space {e} with ⊥ = {e}.

pub fn multiply(&self, a: usize, b: usize) -> usize

Multiply two elements.

pub fn closure(&self, subset: &[bool]) -> Vec<bool>

Closure A^⊥⊥: double orthogonal of a subset A ⊆ M. First computes A^⊥ = {m | ∀ a ∈ A, m·a ∈ ⊥}, then its orthogonal.

pub fn orthogonal(&self, subset: &[bool]) -> Vec<bool>

Orthogonal: A^⊥ = {m | ∀ a ∈ A, m·a ∈ ⊥}.

pub fn is_fact(&self, subset: &[bool]) -> bool

Check whether a subset is a fact (= ⊥-closed, i.e., A = A^⊥⊥).

pub fn subset_size(subset: &[bool]) -> usize

Count elements in a subset.

Trait Implementations

impl Clone for PhaseSpace

fn clone(&self) -> PhaseSpace

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for PhaseSpace

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

Formats the value using the given formatter.