The weight vector should be totally positive, even in the homogeneous case. The result may or may not be a monomial ideal. When a weight vector is not specified, this simply uses the current term order.
i1 : R = ZZ/32003[symbol a..symbol d]
o1 = R
o1 : PolynomialRing
|
i2 : inL = {c^4, b*d^2, b*c, b^2*d, b^3}
4 2 2 3
o2 = {c , b*d , b*c, b d, b }
o2 : List
|
i3 : L = {c^4-a*d^3, -c^3+b*d^2, b*c-a*d, -a*c^2+b^2*d, b^3-a^2*c}
4 3 3 2 2 2 3 2
o3 = {c - a*d , - c + b*d , b*c - a*d, - a*c + b d, b - a c}
o3 : List
|
i4 : weightVector(inL,L)
o4 = {8, 8, 3, 1}
o4 : List
|
i5 : groebnerCone(inL,L)
o5 = (| 0 0 |, | 1 0 |)
| 0 0 | | 0 1 |
| -2 -3 | | -2 3 |
| -3 -4 | | -3 4 |
o5 : Sequence
|
i6 : initialIdeal({8,8,3,1},ideal L)
2 4 2 3
o6 = ideal (b*d , b*c, c , b d, b )
o6 : Ideal of R
|
i7 : initialIdeal({5,5,2,1},ideal L)
2 4 3 2 3
o7 = ideal (b*c, b*d , c - a*d , b d, b )
o7 : Ideal of R
|