Struct ChainComplex 

pub struct ChainComplex {
    pub groups: Vec<ChainGroup>,
    pub boundaries: Vec<Vec<Vec<i64>>>,
}

A chain complex C_• with boundary maps d_n : C_n → C_{n-1}.

Stored as a sequence of groups and the matrices representing the boundary maps. boundaries[i] is the matrix of d_{i+1} : C_{i+1} → C_i (rows = rank C_i).

Fields

groups: Vec<ChainGroup>

The chain groups C_0, C_1, …, C_n.

boundaries: Vec<Vec<Vec<i64>>>

Boundary matrices d_1, d_2, …, d_n (one fewer than groups).

Implementations

impl ChainComplex

pub fn new() -> Self

Create an empty chain complex.

pub fn add_group(&mut self, rank: usize, name: &str)

Append a chain group C_k with the given rank and label.

pub fn add_boundary(&mut self, matrix: Vec<Vec<i64>>)

Append a boundary matrix d_k : C_k → C_{k-1}.

The matrix is stored as a list of rows (each row has rank(C_{k-1}) entries and there are rank(C_k) columns).

pub fn compute_betti_numbers(&self) -> Vec<i64>

Compute the Betti numbers β_n = dim ker(d_n) - dim im(d_{n+1}).

Convention: boundaries[k] = d_{k+1}: C_{k+1} → C_k. So d_i = boundaries[i-1] and d_{i+1} = boundaries[i].

Returns one Betti number per chain group.

pub fn euler_characteristic(&self) -> i64

Compute the Euler characteristic χ = ∑_n (-1)^n β_n.

pub fn is_exact_at(&self, n: usize) -> bool

Check whether the complex is exact at position n (0-indexed).

Exactness at C_n means im(d_{n+1}) = ker(d_n), i.e. β_n = 0.

Trait Implementations

impl Clone for ChainComplex

fn clone(&self) -> ChainComplex

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ChainComplex

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

Formats the value using the given formatter.

impl Default for ChainComplex

fn default() -> ChainComplex

Returns the “default value” for a type.