permaviss.persistence_algebra.module_persistence_homology¶
module_persistence_homology.py
This module implements the persistence module homology
Functions
module_persistence_homology (D, Base, p) |
Given the differentials of a chain of tame persistence modules, we compute barcode bases for the homology of the chain. |
quotient (M, N, p) |
Assuming that N generates a submodule of M, we compute a barcode basis for the quotient M / N. |
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permaviss.persistence_algebra.module_persistence_homology.
module_persistence_homology
(D, Base, p)[source]¶ Given the differentials of a chain of tame persistence modules, we compute barcode bases for the homology of the chain.
Parameters: - D (
list(Numpy Array)
) – List of differentials of the chain complex. - Base (
Numpy Array
) – List containing barcode bases for each dimension - p (int(prime)) – Prime number to perform arithmetic mod p
Returns: - Hom (
list(barcode_basis)
) – Cycles mod boundaries of differentials, starting with: birth rad, death rad. If a cycle does not die we put max_rad as death radius. - Im (
list(barcode_basis)
) – List storing bases for the images of differentials - PreIm (
list(Numpy Array)
) – List storing bases for the preimages of the differentials. That is, which generators produce each image generator. This leads to how to go back from boundaries to preimages.
- D (
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permaviss.persistence_algebra.module_persistence_homology.
quotient
(M, N, p)[source]¶ Assuming that N generates a submodule of M, we compute a barcode basis for the quotient M / N.
Parameters: - M (
barcode_basis
) – Basis for module - N (
barcode_basis
) – Basis for submodule of N - p (int(prime)) –
Returns: Q – Barcode basis for the quotient M / N
Return type: barcode_basis
- M (