Papers by Julio cesar Chico rubio
Journal of Symbolic Computation, 2006
In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp ... more 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 user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and Eilenberg-Moore spectral sequences, in particular the E r p,q and d r p,q for arbitrary r. They also determine when E r p,q = E ∞ p,q and describe the filtration of the target homology groups H p+q by the E ∞ p,q 's.
Bulletin des Sciences Mathématiques, 2002
The classical "computation" methods in Algebraic Topology most often work by means of highly infi... more The classical "computation" methods in Algebraic Topology most often work by means of highly infinite objects and in fact are not constructive. Typical examples are shown to describe the nature of the problem. The Rubio-Sergeraert solution for Constructive Algebraic Topology is recalled. This is not only a theoretical solution: the concrete computer program Kenzo has been written down which precisely follows this method. This program has been used in various cases, opening new research subjects and producing in several cases significant results unreachable by hand. In particular the Kenzo program can compute the first homotopy groups of a simply connected arbitrary simplicial set. * This text was used as a background paper for a plenary talk of the second author during the EACA Congress of Tenerife, September 1999. A "general public" version has appeared in [20]; it is an excellent introduction for the present text.
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Papers by Julio cesar Chico rubio