-- -*- M2-comint -*- hash: 10923277865167169944

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)

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")

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)

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

o9 : Ideal of R

i10 : 
