
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

