[Axiom-math] Re: multivariate resultants

[Amit Khetan]

Hi Tim,

I do have a MAPLE 7 implementation of my bivariate resultant
code. I have included it in my email. Let me know if you have
any troubles with it. I would also be happy to answer any other
questions about the algorithm you might have.

By the way what are the applications of resultants you are interested
in?

Amit

On Wed, 28 Jul 2004, Tim Daly wrote:

> 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
>
> ===================================================================
>
> 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
>

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