Type Alias SimplicialComplex 

pub type SimplicialComplex = Complex<Simplex>;

A type alias for a simplicial complex.

Aliased Type

pub struct SimplicialComplex {
    pub attachment_lattice: Lattice<usize>,
    pub elements: HashMap<usize, Simplex>,
    pub next_id: usize,
}

Fields

attachment_lattice: Lattice<usize>

The attachment relationships between elements, represented as a lattice of element IDs.

This lattice encodes the face relation: if element a is a face of element b, then attachment_lattice.leq(a.id(), b.id()) returns Some(true).

Using IDs rather than full elements provides:

• Memory efficiency: IDs are much smaller than full elements
• Performance: Integer comparisons are faster than element comparisons
• Flexibility: Lattice operations independent of element type

elements: HashMap<usize, Simplex>

A map storing all elements in the complex, keyed by their assigned ID.

This provides:

• Fast lookup: O(1) access to elements by ID
• Rich operations: Access to full element data and methods
• Content queries: Iteration over elements by dimension, type, etc.

next_id: usize

The counter for the next available unique element identifier.

This ensures that:

• Each element gets a unique ID when added
• IDs are assigned sequentially for predictable behavior
• The complex can manage arbitrary numbers of elements