toricSyz -- Calculate toric syzygies of monomials in the initial algebra.

Synopsis

• Usage:

  result = toricSyz(subR, M)

• Inputs:
  • subR, an instance of the type Subring, generated by a sagbi basis.
  • M, a matrix, a 1$\times$r matrix of monomials in the initial algebra of subR.
• Outputs:
  • result, a matrix, the syzygies of M in the rank-r free module over the initial algebra.

Description

i1 : R = QQ[t_1,t_2];

i2 : A = subring sagbi{t_1^2,t_1*t_2,t_2^2};

i3 : M = matrix{{t_1^2, t_1*t_2}};

             1       2
o3 : Matrix R  <--- R

i4 : toricSyz(A, M)

o4 = | -t_2^2  t_1t_2 |
     | -t_1t_2 t_1^2  |

             2       2
o4 : Matrix R  <--- R