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) -- the Graver basis using temporary file name /tmp/M2-953-0/0 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 : toricGraverDegrees(A) -- just the degrees ------------------------------------------------- 4ti2 version 1.6.2, Copyright 2006,2013 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. ------------------------------------------------- Norm = 4, number of elements = 3 Norm = 6, number of elements = 2 using temporary file name /tmp/M2-953-0/1 |
Note that these are all 1-norms of the vectors. Since IA is homogeneous, there are 3 binomials of degree 2 (norm 4) and 2 binomials of degree 3 (norm 6).
i4 : M = matrix "1,1,1,1,1,1,1,1,1,1,1; 1,1,1,1,0,0,0,0,0,0,0; 0,0,0,0,1,1,1,0,0,0,0; 0,0,0,0,0,0,0,1,1,1,1; 1,2,3,4,1,2,3,1,2,3,4" o4 = | 1 1 1 1 1 1 1 1 1 1 1 | | 1 1 1 1 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 1 0 0 0 0 | | 0 0 0 0 0 0 0 1 1 1 1 | | 1 2 3 4 1 2 3 1 2 3 4 | 5 11 o4 : Matrix ZZ <--- ZZ |
i5 : toricGraverDegrees(M) ------------------------------------------------- 4ti2 version 1.6.2, Copyright 2006,2013 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. ------------------------------------------------- Norm = 4, number of elements = 37 Norm = 6, number of elements = 115 Norm = 8, number of elements = 76 Norm = 10, number of elements = 15 using temporary file name /tmp/M2-953-0/2 |
i6 : A = matrix "1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0;0,1,1,0,0,0,0,0,0,1,0,1,1,0,1,0,0,0;0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,1,0,1;0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,1,1;0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0;1,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0;0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1,1;0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,1,0,1;0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1"; 9 18 o6 : Matrix ZZ <--- ZZ |
i7 : toricGraverDegrees(A) ------------------------------------------------- 4ti2 version 1.6.2, Copyright 2006,2013 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. ------------------------------------------------- Norm = 4, number of elements = 9 Norm = 6, number of elements = 67 Norm = 8, number of elements = 378 Norm = 10, number of elements = 792 Norm = 12, number of elements = 1800 Norm = 14, number of elements = 1872 Norm = 16, number of elements = 1224 Norm = 18, number of elements = 792 Norm = 20, number of elements = 432 Norm = 22, number of elements = 96 using temporary file name /tmp/M2-953-0/3 |