Le séminaire a lieu le mardi à 11 h 45 (sauf modification exceptionnelle), au campus Côte de Nacre, bâtiment Sciences 3, salle S3 351, 3ème étage.
Irreducibility of polynomials over the rationals is an important
subject in mathematics, with many applications in computer algebra
and algorithmics. This is a well established research area
requiring different concepts and tools from many fields.
Although it is well known that "almost" every rational
polynomial is irreducible, it is not easy to decide if a single
polynomial is so. In this talk, we first recall some classical
criteria for irreducibility. Then, we focus on the reciprocal case,
and describe new irreducible criteria we have obtained in this
context. This leads us to a new characterization of cyclotomic
polynomials in terms of linear algebra. We finally discuss the
possible consequences of our work in algorithmics and computer
Joint work with Eda Cesaratto (UNGS and CONICET).