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

Usage:

toBinomial(M,R)
Inputs:
- M, a matrix,
- R, a ring, ring with as least as many generators as the columns of M
Outputs:
- I, an ideal,

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

The source of this document is in FourTiTwo.m2:341:0.