# 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.
`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 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.
`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)) – Q – Barcode basis for the quotient M / N `barcode_basis`