[Axiom-math] multivariate resultants

[Tim Daly]

I've been skimming Khetan's PhD thesis (formulas for resultants).
In it he shows how to find the resultants for 2 and 3 dimensions.
It appears there is a clever rewrite using a change of variables
which I don't quite understand. However, once that is done the
formulas seem rather straightforward to compute. I'm going to
try a few 2D trivial examples by hand and see what I get. It's
not quite what you want but it's a start.

Tim

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I believe he was talking about

Efficient Incremental Algorithms for the Sparse Resultant and the Mixed Volume,
with J. Canny, JSC'95 (ps.gz, pdf). Prelim. conference version: Practical
Method for the Sparse Resultant, with J. Canny, ACM ISSAC'93 (ps.gz, pdf).

A Subdivision-Based Algorithm for the Sparse Resultant, with J.F. Canny,
J.ACM'00 (ps.gz, pdf). Initial AAECC conference version: An Efficient Algorithm
for the Sparse Mixed Resultant, with J. Canny (ps.gz, pdf).
 
Improved computation of determinants and resultants, with V. Pan: CASC (ps.gz),
full version (ps.gz).

which are all available online from

http://cgi.di.uoa.gr/~emiris/publis.html



The algorithm of Khetan is described in

The resultant of an unmixed bivariate system Journal of Symbolic Computation
36, 425-442 PS , PDF

available online from

http://www.math.umass.edu/~khetan/papers.html

It seems to me that this one is less work, but I don't really know.

Martin