Computer Algebra
Francois.Boulier@univ-lille1.fr
Alexandre.Sedoglavic@univ-lille1.fr
Algebraic elimination. Gröbner bases
Gröbner bases were invented by Bruno Buchberger, in 1965, as a tool for studying the ideals generated by many different polynomials, in many different variables. Nowadays, Gröbner bases are a very important tool, as well theoretical, as practical, for solving systems of polynomial equations. Generalizations of Gröbner bases for systems of polynomial differential equations are one of the specialties of the computer algebra team of the LIFL.
Very few algorithms exist for computing Gröbner bases: the Buchberger algorithm, a few other algorithms developed by Faugère at the LIP6. Recently, a new algorithm, by S. Gao, Y.Guan F. Volny and M. Wang, was designed, with very promising performances.
The training could be continued in a PhD thesis