## Section: Software

### Multires , a Maple package for multivariate resolution problems

Participants : Laurent Busé [ contact person ] , Bernard Mourrain.

http://www-sop.inria.fr/galaad/software/multires/ .

The Maple package multires contains a set of routines related to the resolution of polynomial equations. The prime objective is to illustrate various algorithms on multivariate polynomials, but not their effectiveness, which is achieved in a more adapted environment such as Mathemagix . It provides methods for building matrices whose determinants are multiples of resultants on certain varieties, and solvers depending on these formulations, and based on eigenvalues and eigenvectors computation. It contains the computations of Bezoutians in several variables, the formulation of Macaulay, Jouanolou for projective resultants, Bezout and (sparse) resultants on a toric variety, residual resultants of complete intersections, functions for computing the degree of residual resultants, algorithms for the geometric decomposition of algebraic varieties. Furthermore, there are tools related to the duality of polynomials, particularly the computation of residues for complete intersections of dimension 0.

Collaborators: Ioannis Emiris, Olivier Ruatta and Philippe Trébuchet.