Local rings of embedding codepth 3: a classification algorithm

Let I be an ideal of a regular local ring Q with residue field k. The length of the minimal free resolution of R=Q/I is called the codepth of R. If it is at most 3, then the resolution carries a structure of a differential graded algebra, and the induced algebra structure on $Tor_Q(R,k) provides for a classification of such local rings. We describe the Macaulay2 package CodepthThree that implements an algorithm for classifying a local ring as above by computation of a few cohomological invariants.