i1 : A = matrix "1,1,1,1; 1,2,3,4"
o1 = | 1 1 1 1 |
| 1 2 3 4 |
2 4
o1 : Matrix ZZ <--- ZZ
|
i2 : toricGroebner(A)
using temporary file name /tmp/M2-10468-0/0
o2 = | -1 1 1 -1 |
| -1 2 -1 0 |
| 0 -1 2 -1 |
3 4
o2 : Matrix ZZ <--- ZZ
|
Note that the output of the command is a matrix whose rows are the exponents of the binomials that for a Groebner basis of the toric ideal IA. As a shortcut, one can ask for the output to be an ideal instead:
i3 : R = QQ[a..d]
o3 = R
o3 : PolynomialRing
|
i4 : toricGroebner(A,R)
using temporary file name /tmp/M2-10468-0/1
2 2
o4 = ideal (b*c - a*d, b - a*c, c - b*d)
o4 : Ideal of R
|
4ti2 offers the use of weight vectors representing term orders, as follows:
i5 : toricGroebner(A,Weights=>{1,2,3,4})
using temporary file name /tmp/M2-10468-0/2
o5 = | -1 1 1 -1 |
| -1 2 -1 0 |
| 0 -1 2 -1 |
3 4
o5 : Matrix ZZ <--- ZZ
|