Struct BipersistenceModule 

pub struct BipersistenceModule { /* private fields */ }

Exact finite H¹ module of a degree-Rips bifiltration.

Cover maps are cohomology restrictions. Their ranks equal the ranks of the dual homology inclusion maps over the same field.

Implementations

impl BipersistenceModule

pub fn class_atlas( &self, base_grade: Bigrade, base_class: &[BipersistenceTerm], ) -> Result<CohomologyClassAtlas>

Compute all extensions of one nonzero class over its upper parameter cone.

impl BipersistenceModule

pub fn circular_coordinate_family( &self, atlas: &CohomologyClassAtlas, params: CircularCoordinateParams, ) -> Result<CircularCoordinateFamily>

Compute checked circular coordinates for every unique atlas extension.

Ambiguous and absent extensions have status CircularCoordinateFamilyStatus::NotAttempted. Every unique extension has a lift failure, solve failure, or success status. A failed computation is reported at its node, and does not discard coordinates computed at other nodes. Automatic family construction requires an odd prime coefficient modulus. Modulus two requires a caller-supplied integral lift and is rejected before any node computation.

impl BipersistenceModule

pub fn from_degree_rips( degree_rips: &DegreeRipsBifiltration, modulus: u32, limits: BipersistenceLimits, ) -> Result<Self>

Construct the complete finite H¹ module on a degree-Rips grid.

Construction checks every cover restriction and every commutative square. The degree-Rips input must include homology dimension one.

pub fn modulus(&self) -> u32

Prime coefficient modulus.

pub fn scales(&self) -> &[f64]

Scale values in strict ascending order.

pub fn minimum_degrees(&self) -> &[usize]

Minimum degrees in strict descending order.

pub fn nodes(&self) -> &[BipersistenceNode]

Nodes in scale-major, then density-major order.

pub fn cover_maps(&self) -> &[BipersistenceMap]

Checked horizontal and vertical cover maps.

pub fn degree_rips(&self) -> &DegreeRipsBifiltration

Source degree-Rips bifiltration.

pub fn node(&self, grade: Bigrade) -> Result<&BipersistenceNode>

Return one module node.

pub fn h1_graph(&self, grade: Bigrade) -> Result<&SparseDistanceMatrix>

Return the zero-weight graph used for H¹ at one grid node.

The graph retains inactive vertices as isolated labels. It represents positive-dimensional flag cohomology, not H⁰ of the degree-Rips slice.

pub fn cohomology_space(&self, grade: Bigrade) -> Result<&CohomologySpace>

Return the canonical H¹ space at one grid node.

pub fn cover_map( &self, lower: Bigrade, upper: Bigrade, ) -> Result<&BipersistenceMap>

Return one checked cover map.

impl BipersistenceModule

pub fn map(&self, lower: Bigrade, upper: Bigrade) -> Result<BipersistenceMap>

Compute the exact map between comparable grades.

The result composes cover maps. Checked commutative squares make the result independent of the chosen monotone path.

pub fn map_rank(&self, lower: Bigrade, upper: Bigrade) -> Result<usize>

Rank of the exact map between comparable grades.

pub fn rectangle_rank(&self, rectangle: BipersistenceRectangle) -> Result<usize>

Compute the generalized rank of one closed rectangle.

The value is the rank of the canonical map from the diagram limit to its colimit. The same value is obtained from the dual homology module.

pub fn region_rank(&self, region: &BipersistenceRegion) -> Result<usize>

Compute the generalized rank of one connected finite region.

The value is the rank of the canonical map from the diagram limit to its colimit. Every comparable pair in the induced subposet contributes its exact module map. A region with a minimum and maximum has the rank of the map between those grades.

Trait Implementations

impl Clone for BipersistenceModule

fn clone(&self) -> BipersistenceModule

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for BipersistenceModule

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

Formats the value using the given formatter.