On the specification for solvers of polynomial systems
Résumé
In this paper, the main different methods for solving polynomial systems (\Gr es, triangular sets,~\ldots) are compared on an example coming from geometry. It is shown that these methods may be combined for automatically studying the number of admissible real solutions of a polynomial system depending on parameters; this study provides as output a description of this number as a function of the parameters.
Mots clés
ensemble triangulaire
base de gröbner
géométrie
inéquation polynomiale
triangle
gröbner basis
système de calcul formel
systeme d'équations polynomiales
système polynomial
équation polynomiale
geometry
polynomial inéquation
polynomial equation
polynomial system solving
algebraic computation
symbolic computation
computer algebra
calcul formel
triangular set