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Re: elimination using GroebnerBasis


On 16 Jul 2004, at 19:06, Gareth Owen wrote:
>
> Am I right in thinking that
>
> GroebnerBasis[{poly1, poly2, poly3},{x,y,z},{z}]
>
> will give a polynomial that is the result of eliminating x and y from 
> the 3
> polynomials together?
> -- 
> Gareth Owen
> Usenet is like Tetris for people who still remember how to read
>
>
You have got the last two arguments wrong way round. You will get two 
polynomials from which z has been eliminated, e.g.

poly1 = x^2 - y^2 - x*y + z^2; poly2 = x + y + z;
   poly3 = x - y + z;


GroebnerBasis[{poly1, poly2, poly3}, {x, y, z}, {z}]


{y, x^2}

If you want to elimnate x and y you should use:


GroebnerBasis[{poly1, poly2, poly3}, {x, y, z}, {x, y}]

{z^2}

or (sometimes more effciently I think)


GroebnerBasis[{poly1, poly2, poly3}, {x, y, z}, {x, 
y},MonomialOrder->EliminationOrder]

{z^2}

another equivalent approach is


First[Eliminate[{poly1, poly2, poly3} == 0, {x, y}]]

z^2


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/


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