Christophe LETELLIER
20/01/2008

G. Gouesbet, S. Meunier-Guttin-Cluzel & C. Letellier

Computer evaluation of Homfly polynomials by using Gauss codes with a skein-template algorithm,

Applied Mathematics and Computation,105, 271-289, 1999. Online

Abstract

Homfly polynomials of knots and links are evaluated on computers by using an algebraic version, with Gauss codes, of the skein-template algorithm. The computer codes are written with the language C whose structure is particularly suitable to such evaluations. Jones, Conway and Alexander polynomials may then be readily obtained as special cases.

L. Le Sceller, C. Letellier & G. Gouesbet

Structure selection for global vector field reconstruction by using the identification of fixed points,

Physical Review E,60(2), 1600-1606, 1999. Online

Abstract

Global vector field reconstruction is a well established technique to provide phenomenological models from nonlinear data, in particular when all information is contained in a so-called standard function. In the case when the standard function is taken as a ratio of polynomials, we establish that information about the fixed points of the system can be automatically retrieved from the data, allowing one to build a better model by selecting an appropriate structure. The method is exemplified in the case of the variablezof the Rössler system, which constitutes a rather acid test case.