Section: New Results

Fast Change of Ordering for Gröbner Bases

Participant : Pierrick Gaudry.

When solving polynomial systems, the usual approach is to compute a Gröbner basis for a monomial order that is compatible with the degree with the F4 or F5 algorithm, and then compute a Gröbner basis for the lexicographical order using the FGLM algorithm. In collaboration with Jean-Charles Faugère, Louise Huot and Guénaël Renault, Pierrick Gaudry designed another approach [27] for this second step, leading to a better asymptotic complexity: the cubic complexity is replaced by the complexity of the linear algebra where the exponent can theoretically be as small as $2.37$.