// get the Groebner basis for an ideal

Q := RationalField();
P<x,y,z,t,u,v> := PolynomialRing(Q, 6);
I := ideal<P |
    x + y + z + t + u + v,
    x*y + y*z + z*t + t*u + u*v + v*x,
    x*y*z + y*z*t + z*t*u + t*u*v + u*v*x + v*x*y,
    x*y*z*t + y*z*t*u + z*t*u*v + t*u*v*x + u*v*x*y + v*x*y*z,
    x*y*z*t*u + y*z*t*u*v + z*t*u*v*x + t*u*v*x*y + u*v*x*y*z + v*x*y*z*t,
    x*y*z*t*u*v - 1>;
time B := GroebnerBasis(I);
B;