/**/ use R ::= QQ[a,b,c];
/**/ I := ideal(b^3+c^21, b^2+a^2+c1, a^2+b^31);
/**/ GF := GroebnerFanIdeals(I);
/**/ [ len(GBasis(I))  I in GF];
[4, 4, 6, 6, 5, 6, 4, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3]
/**/ OrdMat(RingOf(GF[1])); > matrix of the termordering
matrix(ZZ,
[[1, 1, 1],
[0, 0, 1],
[0, 1, 0]])
 The ideal in [Sturmfels, Example 3.9] has 360 marked reduced Groebner bases
/**/ use R ::= QQ[a,b,c];
/**/ I := ideal(a^5+b^3+c^21, b^2+a^2+c1, c^3+a^6+b^51);
/**/ GF := GroebnerFanIdeals(I);
/**/ len(GF);
360
