C = cycleIdeal V
C = cycleIdeal M
C = cycleIdeal P
C = cycleIdeal S
A cycle ideal is the toric ideal generated by the cycles of the bipartite nonincidence graph on vertices/elements and facets/hyperplanes. Each cycle binomial has coefficients coming from the entries of a slack matrix of a realization of the given object. This method computes the cycle ideal of the given realization of a polytope or matroid.


You can create the cycle ideal of any matrix, even if it is not the realization of some matroid or polytope.


Variables in the cycle ideal C will be labelled according to the labeling assigned by symbolicSlackMatrix, which is in order by rows, so to test equality of C with some precomputed ideal care needs to be taken that variable labels match.
If Object => abstractPolytope is chosen, the graphic ideal will be returned instead.
The object cycleIdeal is a method function with options.