Re: elimination using GroebnerBasis
- To: mathgroup at smc.vnet.net
- Subject: [mg49374] Re: [mg49352] elimination using GroebnerBasis
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sat, 17 Jul 2004 06:38:38 -0400 (EDT)
- References: <200407161006.GAA24818@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
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/
- References:
- elimination using GroebnerBasis
- From: Gareth Owen <usenet@gwowen.freeserve.co.uk>
- elimination using GroebnerBasis