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 60 articles , 1 standard article )

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  1. Romero, Ana; Rubio, Julio; Sergeraert, Francis: An implementation of effective homotopy of fibrations (2019)
  2. Denham, Graham (ed.); Gaiffi, Giovanni (ed.); Jímenez Rolland, Rita (ed.); Suciu, Alexander I. (ed.): Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018 (2018)
  3. Feragen, Aasa (ed.); Hotz, Thomas (ed.); Huckemann, Stephan (ed.); Miller, Ezra (ed.): Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 (2018)
  4. Romero, Ana; Sergeraert, Francis: A Bousfield-Kan algorithm for computing the \textiteffectivehomotopy of a space (2017)
  5. Gao, Man; Wu, Jie: Simplicial monoid actions and associated monoid constructions (2016)
  6. Lienhardt, Pascal; Peltier, Samuel: Homology computation during an incremental construction process (2016)
  7. Heras, Jónathan; Martín-Mateos, Francisco Jesús; Pascual, Vico: Modelling algebraic structures and morphisms in ACL2 (2015)
  8. Romero, Ana; Sergeraert, Francis: A combinatorial tool for computing the effective homotopy of iterated loop spaces (2015)
  9. Ellis, Graham; Hegarty, Fintan: Computational homotopy of finite regular CW-spaces (2014)
  10. 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)
  11. Mikhailov, R.: Homotopical and combinatorial aspects of the theory of normal series in groups. (2014)
  12. Poza, María; Domínguez, César; Heras, Jónathan; Rubio, Julio: A certified reduction strategy for homological image processing (2014)
  13. Lambán, Laureano; Martín-Mateos, Francisco J.; Rubio, Julio; Ruiz-Reina, José-Luis: Certified symbolic manipulation: bivariate simplicial polynomials (2013)
  14. Romero, Ana; Rubio, Julio: Homotopy groups of suspended classifying spaces: an experimental approach (2013)
  15. Wu, J.; Mikhailov, R. V.: Homotopy groups as centers of finitely presented groups. (2013)
  16. Álvarez, Víctor; Armario, José Andrés; Frau, María Dolores; Real, Pedro: Homological models for semidirect products of finitely generated Abelian groups. (2012)
  17. Berciano, A.; Molina-Abril, H.; Real, P.: Searching high order invariants in computer imagery (2012)
  18. Domínguez, César; Duval, Dominique: A parameterization process: from a functorial point of view (2012)
  19. Heras, Jónathan; Poza, María; Rubio, Julio: Verifying an algorithm computing discrete vector fields for digital imaging (2012)
  20. Lambán, Laureano; Martín-Mateos, Francisco-Jesús; Rubio, Julio; Ruiz-Reina, José-Luis: Formalization of a normalization theorem in simplicial topology (2012)

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