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
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
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 variable z of the Rössler system, which constitutes a rather acid test case.