It would be nice to implement multivariate resultants, Bezoutians, and sparse resultants. Laurent Buse has written code for this in the past. We hope to provide a package, Resultants, which will do this. If you are willing to help write this, please contact the author if this package!
This documentation describes version 1.0 of Elimination.
The source code from which this documentation is derived is in the file Elimination.m2.