Struct FinitePartialOrder 

pub struct FinitePartialOrder {
    pub size: usize,
    pub le: Vec<Vec<bool>>,
}

A partial order on a finite set, stored as an adjacency matrix.

Fields

size: usize

Number of elements.

le: Vec<Vec<bool>>

The order relation as a boolean matrix: le[i][j] = (i ≤ j).

Implementations

impl FinitePartialOrder

pub fn discrete(n: usize) -> Self

Create the discrete partial order (only x ≤ x for all x).

pub fn is_reflexive(&self) -> bool

Check reflexivity: x ≤ x for all x.

pub fn is_antisymmetric(&self) -> bool

Check antisymmetry: x ≤ y and y ≤ x implies x = y.

pub fn is_transitive(&self) -> bool

Check transitivity: x ≤ y and y ≤ z implies x ≤ z.

pub fn is_valid(&self) -> bool

Check if this is a valid partial order.

pub fn is_total(&self) -> bool

Check totality: x ≤ y or y ≤ x for all x, y.

pub fn maximal_elements(&self) -> Vec<usize>

Find all maximal elements (elements with nothing strictly above them).

pub fn transitive_closure(&self) -> FinitePartialOrder

Compute the transitive closure using Floyd-Warshall.