Abstract
This work integrates the Kenzo system within Sagemath as an interface and an optional package. Our work makes it possible to communicate both computer algebra programs and it enhances the SageMath system with new capabilities in algebraic topology, such as the computation of homotopy groups and some kind of spectral sequences, dealing in particular with simplicial objects of an infinite nature. The new interface allows computing homotopy groups that were not known before.
Highlights
Computational algebraic topology is an active area of research in mathematics with numerous applications in different fields, ranging from data analysis [1] to image processing [2]
Effective homology is a technique developed by Sergeraert [6] which permits carrying out some kinds of computations over infinite structures, via a homotopy equivalence between chain complexes
The wedge construction is implemented in SageMath for finite simplicial sets, but we have considered including the wedge Kenzo construction so that it can be applied to spaces of an infinite nature
Summary
Computational algebraic topology is an active area of research in mathematics with numerous applications in different fields, ranging from data analysis [1] to image processing [2]. In the particular case of algebraic topology, SageMath includes modules for different classes of complexes (simplicial, ∆, and cubical), and simplicial sets (plus other topological objects of different nature, such as knots, links, and braids for example) From these objects, SageMath can compute invariants such as their homology, both by using custom written code or by leveraging an interface to CHomP [3]. The interface allows computing homotopy groups that were not known before This way, this work aims to solve the limitations of SageMath on computations in algebraic topology, by integrating most of the computational features of Kenzo, and some of its external modules in SageMath. We expect to extend the use of Kenzo to a broader community, allowing in this way further new applications in both research and education To this end, both programs are connected via the ECL library (a library interface to Embeddable Common Lisp).
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