Incidence Simplicial Matrices Formalized in Coq/SSReflect

Simplicial complexes are at the heart of Computational Algebraic Topology, since they give a concrete, combinatorial description of otherwise rather abstract objects which makes many important topological computations possible. The whole theory has many applications such as coding theory, robotics o...

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Bibliographic Details
Published inIntelligent Computer Mathematics pp. 30 - 44
Main Authors Heras, Jónathan, Poza, María, Dénès, Maxime, Rideau, Laurence
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Chain Complex
Homology Group
Incidence Matrix
Simplicial Complex
Type Object
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Summary:Simplicial complexes are at the heart of Computational Algebraic Topology, since they give a concrete, combinatorial description of otherwise rather abstract objects which makes many important topological computations possible. The whole theory has many applications such as coding theory, robotics or digital image analysis. In this paper we present a formalization in the Coq theorem prover of simplicial complexes and their incidence matrices as well as the main theorem that gives meaning to the definition of homology groups and is a first step towards their computation.
Bibliography:Partially supported by Ministerio de Educación y Ciencia, project MTM2009-13842- C02-01, and by European Community FP7, STREP project ForMath.
ISBN:9783642226724
3642226728
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-22673-1_3