"Computer Algebra and Resultants"
Universidad de Buenos Aires
A resultant is, informally, a polynomial in the coefficients of a collection of polynomials (typically, n+1 polynomials in n variables) whose vanishing is a necessary and sufficient condition for the existence of a common root of the polynomials. Resultants generalize the notion of the determinant of a linear system and provide a computational tool for polynomial system solving through the elimination of variables.
The study of resultants goes back to classical work of Cayley, Sylvester, Poisson, Bezout, Macaulay and Dixon. In the last decade, there has been a renewed interest both in developing "tailored" resultants associated to special families of input polynomials as well as in finding explicit formulas for their computation.
In this talk, I will survey recent developments in the theory of multidimensional resultants, while trying to give a unified vision of different matrix formulations.