Module cell_complex 

CW complex and cell complex geometry.

This module implements the algebraic machinery of CW complexes and their homological invariants:

• CwCell: Cells of any dimension (vertices, edges, faces, n-cells).
• CwComplex: CW complex with attaching maps and cellular chain complex.
• ChainComplex: Abstract chain complex with boundary maps.
• CellularHomology: Smith normal form and Betti number computation.
• SimplexBoundary: Oriented simplex boundary operator.
• DualComplex: Dual cell decomposition and Hodge duality.
• CoboundaryOperator: Coboundary maps and cohomology groups.
• EulerCharacteristic: Euler characteristic and Euler-Poincaré formula.
• CellularApproximation: Cellular approximation and homotopy equivalence.
• ShellableComplex: Shellability, h-vector, f-vector, Dehn-Sommerville.

Structs

CellularApproximation

Cellular approximation theorem and homotopy equivalence.

CellularHomology

Cellular homology computation via Smith Normal Form.

ChainComplex

An abstract chain complex (C_k, ∂_k) over the integers.

CoboundaryOperator

Coboundary operator δ^k : C^k → C^{k+1} (transpose of boundary ∂_{k+1}).

CwCell

A single cell in a CW complex of dimension dim.

CwComplex

A CW complex represented by its cells, organised by dimension.

DualComplex

Dual cell decomposition of a CW complex.

EulerCharacteristic

Euler characteristic and Euler-Poincaré theorem.

OrientedSimplex

Oriented simplex and its boundary operator.

ShellableComplex

Shellable simplicial complex with f-vector and h-vector.

SimplexBoundary

Simplicial boundary operator as an integer matrix.

Functions

rank_of_matrix

Integer matrix rank via Gaussian elimination over Z (approximate: uses GCD rows).

smith_normal_form

Compute the Smith Normal Form of an integer matrix.