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Re: Multivariate polynomial elimination question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74837] Re: [mg74820] Multivariate polynomial elimination question
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Sat, 7 Apr 2007 04:05:48 -0400 (EDT)
*References*: <200704060824.EAA09273@smc.vnet.net>
On 6 Apr 2007, at 17:24, Paul T wrote:
> I have a polynomial P[x,a,b] with rational coefficents of degree 15 in
> x. It is quartic w.r.t. the variable a, and a cubic w.r.t. b^2. I wish
> to recover the degree 60 and degree 90 (w.r.t. x) polynomials Q[x,b]
> and R[x,a] by eliminating a and b^2 respectively. I've tried naively
> using Eliminate[P==0,a] but this just returns TRUE. Is it possible to
> do this by some other means?
>
>
This sort of elimination is one of the main things that the Groebner
basis algorithm is used for. However, whether Mathematica's
GroebnerBasis will be able to deal with your problem or not in a
reasonable time can't be known without trying your concrete example.
If you would rather try it yourself or think it is too long to post
it here then provide an analogous simpler example and I will show you
how to use GroebnerBasis to do the elimination. You could also search
the archives where there are quite many examples of this kind, or
look at any decent book on algorithmic algebra, e.g. Ideals,
Varieties and Algorithms by Cox, Little and O'Shea.
Andrzej Kozlowski
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