resultants

-*- M2 -*-

Title: Resultants, discriminants, and Chow forms

Description:

An M2 package on resultants/discriminants/Chow forms.  As far as I'm aware there
is a rather old M2 code by Laurent Bus\'e (on his web page) computing
Bezoutians, Macaulay resultants, etc but one could probably try to salvage it
and mainly add lots of new things to it, and do things better now (use BGG,
A-discriminants, etc)

--Mike: Laurent Buse <lbuse@math.unice.fr> is still interested in this.

=============================================================================

Proposed by: Sorin Popescu <sorin@math.sunysb.edu>
Potential Advisor: Mike Stillman
Project assigned to: Daniel Giaimo <dgiaimo@gmail.com>
Current status: just started (12 Jan 2011)

=============================================================================

Progress log:

Comments to Dan Giaimo from Mike, 12 Jan 2011:

	 I did write some engine code to help with construction of these matrices, but
	 did not go further than that, but we should use that code when rewriting
	 Laurent Buse's code.

	 I see several things to do:

	 0. make a package, design an interface that we will like to use

	 1. get Laurent's code working on a modern M2, in this package
	  (I think this includes Macaulay, and Bezoutian forms).

	  2. we need examples for testing!

	  3. possibly add in the sparse (toric) resultant.

	  4. possibly add in the "other" forms for resultants (e.g. from
	  Eisenbud-Schreyer, or GKZ discriminants book, see also recent papers of
	  D'Andrea and co-authors).

	  5. the determinant of a complex (possibly this should be its own package.  This
	  would be very useful).