-- -*- M2-comint -*- {* hash: 674048408 *}

i1 : A = matrix"1,1,1,1;0,1,2,3"

o1 = | 1 1 1 1 |
     | 0 1 2 3 |

              2        4
o1 : Matrix ZZ  <--- ZZ

i2 : R = QQ[a..d]

o2 = R

o2 : PolynomialRing

i3 : M = toricMarkov(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.
-------------------------------------------------
Using 64 bit integers.
4ti2 Total Time:  0.00 secs.
using temporary file name /tmp/M2-3657-1

o3 = | 0 1  -2 1 |
     | 1 -2 1  0 |
     | 1 -1 -1 1 |

              3        4
o3 : Matrix ZZ  <--- ZZ

i4 : I = toBinomial(M,R)

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

o4 : Ideal of R

i5 : B = syz A

o5 = | -1 2  |
     | 2  -3 |
     | -1 0  |
     | 0  1  |

              4        2
o5 : Matrix ZZ  <--- ZZ

i6 : N = toricMarkov(transpose B, InputType => "lattice")
-------------------------------------------------
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.
-------------------------------------------------
Using 64 bit integers.
4ti2 Total Time:  0.00 secs.
using temporary file name /tmp/M2-3657-2

o6 = | 0 1  -2 1 |
     | 1 -2 1  0 |
     | 1 -1 -1 1 |

              3        4
o6 : Matrix ZZ  <--- ZZ

i7 : J = toBinomial(N,R) -- toricMarkov(transpose B, R, InputType => "lattice")

               2           2
o7 = ideal (- c  + b*d, - b  + a*c, - b*c + a*d)

o7 : Ideal of R

i8 : I == J

o8 = true

i9 : toricMarkov(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.
-------------------------------------------------
Using 64 bit integers.
4ti2 Total Time:  0.00 secs.
using temporary file name /tmp/M2-3657-3

               2           2
o9 = ideal (- c  + b*d, - b  + a*c, - b*c + a*d)

o9 : Ideal of R

i10 :