This directory contains sources for the compsysmed/primdecomp container.
It implements an algorithm for MHS generation based on computational algebra in Macaulay2.
Specifically, we construct a monomial ideal with one generator for each edge of the input hypergraph, then compute its associated primes, which correspond to MHSes.
For example, suppose our input hypergraph is H = [[1, 2, 5], [2, 3, 4], [1, 3]]. In Macaulay2, we first construct the monomial ring:
> k = QQ[x1, x2, x3, x4, x5]
We then construct the ideal representing H:
> I = monomialIdeal(x1*x2*x5, x2*x3*x4, x1*x3)
Finally, we compute the associated primes, which correspond to the MHSes [[1, 2], [1, 3], [1, 4], [2, 3], [3, 5]].
> P = associatedPrimes I
{monomialIdeal (x1, x2), monomialIdeal (x1, x3), monomialIdeal (x1, x4), monomialIdeal (x2, x3), monomialIdeal (x3, x5)}
The src/mhs script, which generates a Macaulay 2 program for an input hypergraph, is Python code written by Andrew Gainer-Dewar and copyright of the Vera-Licona Research Group.
To build the container yourself, run the following from this directory:
docker build -t compsysmed/primdecomp:latest .
You do not need to build the container yourself to use the algorithms. You can fetch a prebuilt copy of the container by running the following:
docker pull compsysmed/primdecomp:latest
The code in this directory is available under the terms of the GPLv3 license.