Spinor groups and algebraic coding theory
Journal of Combinatorial Theory Series A
Discrete Applied Mathematics
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
A modular formalisation of finite group theory
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Effective homology of bicomplexes, formalized in Coq
Theoretical Computer Science
Algebraic topological analysis of time-sequence of digital images
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
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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.