# toBinomial -- creates a toric ideal from a given set of exponents of its generators

## Synopsis

• Usage:
toBinomial(M,R)
• Inputs:
• M, ,
• R, a ring, ring with as least as many generators as the columns of M
• Outputs:

## Description

Equivalent to "output --binomials" in 4ti2. Returns the ideal in the ring R generated by the binomials corresponding to rows of M.

 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 : B = syz A o2 = | 1 2 | | -2 -3 | | 1 0 | | 0 1 | 4 2 o2 : Matrix ZZ <--- ZZ i3 : R = QQ[a..d] o3 = R o3 : PolynomialRing i4 : toBinomial(transpose B,R) 2 3 2 o4 = ideal (- b + a*c, - b + a d) o4 : Ideal of R

## Ways to use toBinomial :

• "toBinomial(Matrix,Ring)"

## For the programmer

The object toBinomial is .