Symbolic Computation Group

The polynomial ideal generated by the minors of a fixed size of a polynomial matrix is called a determinantal ideal. These ideals arise naturally in a variety of scientific contexts, including real algebraic geometry and optimization. When using a signature-based Gröbner basis algorithm such as F5 to compute a grevlex Gröbner basis for such ideals, many reductions to zero are encountered since determinantal ideals cannot, in general, be generated by a regular sequence. In this talk, I will give refined versions of the F5 Gröbner basis algorithm adapted to specific kinds of determinantal varieties, and apply these new algorithms to the problem of computing the critical points of a polynomial restricted to an algebraic set.

This talk is based on joint work with Vincent Neiger and Mohab Safey El Din.