Integration of the Kenzo System within SageMath for New Algebraic Topology Computations

Julián Cuevas-Rozo, Jose Divasón, Miguel Marco-Buzunáriz and Ana Romero
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Julián Cuevas-Rozo: Department of Mathematics and Computer Science, University of La Rioja, 26006 Logroño, Spain
Jose Divasón: Department of Mathematics and Computer Science, University of La Rioja, 26006 Logroño, Spain
Miguel Marco-Buzunáriz: Department of Mathematics, University of Zaragoza, 50009 Zaragoza, Spain
Ana Romero: Department of Mathematics and Computer Science, University of La Rioja, 26006 Logroño, Spain

Mathematics, 2021, vol. 9, issue 7, 1-24

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.

Keywords: computer algebra; Kenzo interface; computational algebraic topology; homotopy groups; spectral sequences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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