# 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 1$\times$r matrix of monomials in the initial algebra of subR.
• Outputs:
• result, , the syzygies of M in the rank-r free module over the initial algebra.

## Description

This is an experimental implementation of algorithm 11.18 in Sturmfels' "Gröbner bases and Convex Polytopes."

 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

See Experimental feature: modules over subrings for another example.

## Ways to use toricSyz :

• "toricSyz(Subring,Matrix)"

## For the programmer

The object toricSyz is .