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}]
but I got different solutions. Any significant about this? I am not
sure if this can help to solve the problem?
Thanks
Col