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# 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

## Ways to use toBinomial:

- `toBinomial(Matrix,Ring)`

## For the programmer

The object toBinomial is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/FourTiTwo.m2:341:0.