Kenzo

The Kenzo program implements the general ideas of the second author about Effective Homology, mainly around the Serre and Eilenberg-Moore spectral sequences. The first author (re-) discovered the importance of the Basic Perturbation Lemma in these questions, already noted by Victor Gugenheim and this program directly implements and directly uses this ”lemma” which should be called the Fundamental Theorem of Algebraic Topology. The first version of the program, called EAT, was written in 1989-90 by the first and the second authors. It has been demonstrated in several universities: France: Grenoble and Montpellier, Belgium: Louvain-la-Neuve, Italy: Genoa and Pisa, Sweden: Stockolm, Japan: Sapporo, Morioka, Urawa, Tokyo, Kyoto, Nara, Osaka and Hiroshima.

This software is also referenced in ORMS.


References in zbMATH (referenced in 49 articles , 1 standard article )

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  1. Heras, Jónathan; Martín-Mateos, Francisco Jesús; Pascual, Vico: Modelling algebraic structures and morphisms in ACL2 (2015)
  2. Romero, Ana; Sergeraert, Francis: A combinatorial tool for computing the effective homotopy of iterated loop spaces (2015)
  3. Ellis, Graham; Hegarty, Fintan: Computational homotopy of finite regular CW-spaces (2014)
  4. Lambán, L.; Rubio, J.; Martín-Mateos, F.J.; Ruiz-Reina, J.L.: Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm (2014)
  5. Poza, María; Domínguez, César; Heras, Jónathan; Rubio, Julio: A certified reduction strategy for homological image processing (2014)
  6. Romero, Ana; Rubio, Julio: Homotopy groups of suspended classifying spaces: an experimental approach (2013)
  7. Wu, J.; Mikhailov, R.V.: Homotopy groups as centers of finitely presented groups. (2013)
  8. Álvarez, Víctor; Armario, José Andrés; Frau, María Dolores; Real, Pedro: Homological models for semidirect products of finitely generated Abelian groups. (2012)
  9. Berciano, A.; Molina-Abril, H.; Real, P.: Searching high order invariants in computer imagery (2012)
  10. Domínguez, César; Duval, Dominique: A parameterization process: from a functorial point of view (2012)
  11. Heras, Jónathan; Poza, María; Rubio, Julio: Verifying an algorithm computing discrete vector fields for digital imaging (2012)
  12. Lambán, Laureano; Martín-Mateos, Francisco-Jesús; Rubio, Julio; Ruiz-Reina, José-Luis: Formalization of a normalization theorem in simplicial topology (2012)
  13. Romero, Ana; Rubio, Julio: Computing the homology of groups: the geometric way. (2012)
  14. Romero, Ana; Sergeraert, Francis: Effective homotopy of fibrations (2012)
  15. Barakat, Mohamed; Lange-Hegermann, Markus: An axiomatic setup for algorithmic homological algebra and an alternative approach to localization (2011)
  16. Breen, Lawrence; Mikhailov, Roman: Derived functors of nonadditive functors and homotopy theory (2011)
  17. Domínguez, César; Rubio, Julio: Effective homology of bicomplexes, formalized in Coq (2011)
  18. Heras, Jónathan; Pascual, Vico; Rubio, Julio: Proving with ACL2 the correctness of simplicial sets in the Kenzo system (2011)
  19. Heras, Jónathan; Pascual, Vico; Rubio, Julio: A system for computing and reasoning in algebraic topology (2011)
  20. Heras, Jónathan; Poza, María; Dénès, Maxime; Rideau, Laurence: Incidence simplicial matrices formalized in Coq/SSReflect (2011)

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