b = isSCM H
This uses the edge ideal notion of sequential CohenMacaulayness; a hypergraph is called SCM if and only if its edge ideal is SCM. The algorithm is based on work of Herzog and Hibi, using the Alexander dual. H is SCM if and only if the Alexander dual of the edge ideal of H is componentwise linear.
There is an optional argument called Gins for isSCM. The default value is false, meaning that isSCM takes the Alexander dual of the edge ideal of H and checks in all relevant degrees to see if the ideal in that degree has a linear resolution. In characteristic zero with the reverselex order, one can test for componentwise linearity using gins, which may be faster in some cases. This approach is based on work of AramovaHerzogHibi and Conca. We make no attempt to check the characteristic of the field or the monomial order, so use caution when using this method.






The object isSCM is a method function with options.