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Topic: Using Groebner Basis routines in Maple
Replies: 0

 Robert H. Lewis Posts: 284 Registered: 12/8/04
Using Groebner Basis routines in Maple
Posted: Jul 9, 2011 9:19 AM

All,

I occasionally use Maple for Groebner basis calculations. I thought I knew what to do, but recently have hit a problem I don't understand.

I am aware of the page

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Groebner/Basis_algorithms

I have a system of equations and I want a GB that will produce one polynomial that contains only the variable ca. (So I want to solve for ca, in essence.) The system of equations is at the end of this note.

I have tried

out := fgb_gbasis(sys, [b, c, d, e, f, rr, t50], [ca]);

out := fgb_gbasis(sys, [b, c, d, e, f, t50, rr], [ca])

out := Basis(sys, prod(tdeg(rr, b, c, d, e, f, t50), tdeg(ca)))

out := Basis(sys, lexdeg([b, c, d, e, f, t50, rr], [ca]));

out := Basis(sys, lexdeg([rr, b, c, d, e, f, t50], [ca]))

out := Basis(sys, plex(rr, b, c, d, e, f, t50, ca))

out := Basis(sys, prod(plex(rr, b, c, d, e, f, t50), plex(ca)))

Nothing works. In all cases, there is no polynomial in the GB containing ONLY ca.

I tried rearranging the order of the equations. I also tried Triangularize, but that crashes Maple after 10 minutes or so. This is Maple12.

Robert H. Lewis

- e^2 + d^2 - 2*ca*b*d + b^2 ,
- t50^2*e^2 - e^2 - 2*t50^2*d*e - 2*d*e - t50^2*d^2 - d^2 + t50^2*c^2 + c^2 - rr*t50^2*c - 2*t50*c
+ rr*c + t50^2 + 1 ,
- t50^2*f^2 - f^2 + t50^2*e^2 + e^2 - 4*t50*e + t50^2 + 1 ,
e^2 - d*e + d^2 - b^2 ,
f^2 + d*f + d^2 - c^2 ,
f^2 - e*f + e^2 - 1,
rr^2 - 3,
t50^6 - 33*t50^4 + 27*t50^2 - 3