Emerson G. Escolar

This is a library consisting of a GAP package and helper scripts for computations involving persistence modules over finite commutative grids. Some of its implemented features are listed below.

1. Basic functionality:
   1. Creation of commutative grids and persistence modules
   2. Reading and writing files that represent persistence modules
   3. Enumeration of interval persistence modules
2. Computation of the interval-decomposable part of a persistence module, using the algorithm in H. Asashiba, M. Buchet, E. G. Escolar, K. Nakashima, and M. Yoshiwaki: "On Interval Decomposability of 2D Persistence Modules", arXiv:1812.05261.
3. Computation of the compressed multiplicity and interval-decomposable approximation over 2 x n grids, as introduced in H. Asashiba, E. G. Escolar, K. Nakashima, and M. Yoshiwaki. "On Approximation of 2D Persistence Modules by Interval-decomposables". arXiv:1911.01637.

Source code available here.

This library implements the "Matrix Method" for computing indecomposable decompositions of persistence modules over commutative ladders of finite type. The main ideas and algorithm can be found in the paper:

H. Asashiba, E.G. Escolar, Y. Hiraoka, and H. Takeuchi. "Matrix Method for Persistence Modules on Commutative Ladders of Finite Type". Japan J. Indust. Appl. Math. (2018). https://doi.org/10.1007/s13160-018-0331-y (Also available here. arXiv version here.)

Source code available here.

This project was partially supported by JST CREST Mathematics 15656429.

Implements the ideas discussed in the paper "Optimal Cycles for Persistent Homology Via Linear Programming".

Source code available here.

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What particular (open-source) license applies for each of the software projects can be found in the individual project sites.

In general, the software above are distributed in the hope that they will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose.