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FourTiTwo :: toricCircuits

toricCircuits -- calculates the circuits of the toric ideal; invokes "circuits" from 4ti2

Synopsis

Description

The circuits are contained in the Graver basis of IA. In fact, they are precisely the primitive binomials in the ideal with minimal support.

A = matrix "1,1,1,1; 1,2,3,4"
C = toricCircuits A

The ideal generated by the circuits of A in general differs from the toric ideal of A. For example:

R = QQ[a..d]
Icircuit = toBinomial(toricCircuits(A), R) -- this is the circuit ideal of A
I = toBinomial(toricMarkov(A), R)
I==Icircuit

The two ideals are not the same. There is a minimal generator of I which is not a circuit:

a*d-b*c % I -- this binomial is in I:
a*d-b*c % Icircuit -- but not in Icircuit:

Ways to use toricCircuits :