# Project : galaad

## Section: Software

Keywords : Polynomial algorithmic, resultant, residue, eigenvalues, interpolation, linear algebra.

### multires, a maple package for multivariate resolution problems

Participants : Laurent Busé, Ioannis Emiris, Bernard Mourrain [contact person], Olivier Ruatta, Philippe Trébuchet.

See multires web site: http://www-sop.inria.fr/galaad/logiciels/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, and is not effectiveness, which is achieved in a more adapted environment as synaps. It provides methods to build 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 [47] for projective resultant, Jouanolou [46] combining matrices of Macaulay type, and Bezout and (sparse) resultant on a toric variety [41], [40]. Also being added are a new construction proposed for the residual resultant of a complete intersection [38], functions for computing the degree of residual resultant illustrated in [39], and the geometric algorithm for decomposing an algebraic variety [44]. The Weierstrass method generalized for several variables (presented in [50]) and a method of resolution by homotopy derived from such generalization are implemented as well. Furthermore, there are tools related to the duality of polynomials, particularly the computation of residue for a complete intersection of dimension 0.