-- -*- M2-comint -*- {* hash: 232114658 *}

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 : toricGraver(A)
-------------------------------------------------
4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
4ti2 comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome
to redistribute it under certain conditions.
For details, see the file COPYING.
-------------------------------------------------


Final basis has 1 inhomogeneous, 10 homogeneous and 0 free elements.
Writing 5 vectors to graver file, with respect to symmetry.

4ti2 Total Time: 0.00 secs
using temporary file name /tmp/M2-3969-1

o2 = | 1 -2 1  0 |
     | 2 -3 0  1 |
     | 1 -1 -1 1 |
     | 0 1  -2 1 |
     | 1 0  -3 2 |

              5        4
o2 : Matrix ZZ  <--- ZZ

i3 : R = QQ[a..d]

o3 = R

o3 : PolynomialRing

i4 : toricGraver(A,R)
-------------------------------------------------
4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
4ti2 comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome
to redistribute it under certain conditions.
For details, see the file COPYING.
-------------------------------------------------


Final basis has 1 inhomogeneous, 10 homogeneous and 0 free elements.
Writing 5 vectors to graver file, with respect to symmetry.

4ti2 Total Time: 0.00 secs
using temporary file name /tmp/M2-3969-2

               2           3    2                   2           3      2
o4 = ideal (- b  + a*c, - b  + a d, - b*c + a*d, - c  + b*d, - c  + a*d )

o4 : Ideal of R

i5 :