groebner Basis

• To: mathgroup at smc.vnet.net
• Subject: [mg13738] groebner Basis
• From: Colin <esroz at csv.warwick.ac.uk>
• Date: Wed, 19 Aug 1998 01:38:28 -0400
• Organization: University of Warwick, UK
• Sender: owner-wri-mathgroup at wolfram.com

```hiya,

I tried to use Groebner Basis to solve a set of polynomials.  In the
process of trying out these two polynomials,

polys = {(Cp^2*(w^2 - w2^2)^2 + 2*Cl*Cp*(w^2 - w2^2)*
(w^2 - w2^2 - Cp*w*w2^2*(Xl + Xp)) +
Cl^2*(w2^4 + w^4*(1 + Cp^2*Rl^2*w2^2) - 2*Cp*w^3*w2^2*(Xl + Xp) +
2*Cp*w*w2^4*(Xl + Xp) +
w^2*w2^2*(-2 + Cp^2*w2^2*Xl^2 + 2*Cp^2*w2^2*Xl*Xp +
Cp^2*w2^2*Xp^2)))*Rtotb-
(Cl^2*Rl*(-w^2 + w2^2 + Cp*w*w2^2*Xp)^2),

Rtota * (Rl^2+(Xl+Xp)^2)-Rl*Xp^2}

GroebnerBasis[{polys}, {Cl,Cs,Rl,Xl,Xs}] where the rest of the symbols
are parameters. (n.b. Cl,Cs,Rl,Xl,Xs are the only variables)

I got as many as 10 solutions!!!

I suspect that the algorithm treats other symbols as variables too. That
is why I got
so many solutions.  In addition, when i extended these polynomials to 6
or 7 different
polynomials with the same sort of degree, it crashed the system!(out of
memory)

1) Is there a way that I can tell the algorithm which symbols are
parameters?

2) I tried using GroebnerBasis[{polys},{variables},{variables to be
eliminated}]