- Usage:
`toricGroebner(A) or toricGroebner(A,R)`

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 : toricGroebner(A) o2 = | -1 1 1 -1 | | -1 2 -1 0 | | 0 -1 2 -1 | 3 4 o2 : Matrix ZZ <--- ZZ |

Note that the output of the command is a matrix whose rows are the exponents of the binomials that for a Groebner basis of the toric ideal *I _{A}*. As a shortcut, one can ask for the output to be an ideal instead:

i3 : R = QQ[a..d] o3 = R o3 : PolynomialRing |

i4 : toricGroebner(A,R) 2 2 o4 = ideal (b*c - a*d, b - a*c, c - b*d) o4 : Ideal of R |

`4ti2` offers the use of weight vectors representing term orders, as follows:

i5 : toricGroebner(A,Weights=>{1,2,3,4}) o5 = | -1 1 1 -1 | | -1 2 -1 0 | | 0 -1 2 -1 | 3 4 o5 : Matrix ZZ <--- ZZ |

It seems that some versions of 4ti2 do not pick up on the weight vector. It may be better to run gb computation in M2 directly with specified weights.

- toricGroebner(Matrix)
- toricGroebner(Matrix,Ring)