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>