45 citations · 80 across the 8 of their papers we have counts for
9 papers
Functional Programming is Free
Francis Sergeraert
A paper has recently been published in SIAM-JC. This paper is faulty: 1) The standard requirements about the definition of an algorithm are not respected, 2) The main point in the…
Effective persistent homology of digital images
Ana Romero, Julio Rubio, Francis Sergeraert
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homolog…
Defining and computing persistent Z-homology in the general case
Ana Romero, Jónathan Heras, Julio Rubio +1
By general case we mean methods able to process simplicial sets and chain complexes not of finite type. A filtration of the object to be studied is the heart of both subjects persi…
Constructive Homological Algebra and Applications
Julio Rubio, Francis Sergeraert
This text was written and used for a MAP Summer School at the University of Genova, August 28 to September 2, 2006. Available since then on the web site of the second author, it ha…
Polynomial-time homology for simplicial Eilenberg-MacLane spaces
Marek Krcal, Jiri Matousek, Francis Sergeraert
In an earlier paper of Cadek, Vokrinek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all…
Computing all maps into a sphere
Martin Čadek, Marek Krčál, Jiří Matoušek +3
Given topological spaces X and Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y . We consider a computational version, wh…
Discrete Vector Fields and Fundamental Algebraic Topology
Ana Romero, Francis Sergeraert
We show in this text how the most important homology equivalences of fundamental Algebraic Topology can be obtained as reductions associated to discrete vector fields. Mainly the h…
Computing spectral sequences
A. Romero, J. Rubio, F. Sergeraert
In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the u…
Algebraic Models for Homotopy Types
Julio Rubio Garcia, Francis Sergeraert
The classical problem of algebraic models for homotopy types is precisely stated, to our knowledge for the first time. Two different natural statements for this problem are produce…