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 the structure of a differential graded algebra, and the induced algebra structure on ${Tor}_{\ast }^Q\left(R,k\right)$ provides for a classification of such local rings.