This means that almost everything I work on eventually involves manipulation of polynomials whose terms are words from some alphabet. Most of this work currently falls under the umbrella of the Hopf project at Va Tech. Opal Opal is a system that I originally developed as part of my Ph.D. work. The main thing it does is compute Groebner bases in path algebras, but we are expanding it to include computations over right modules of path algebras. I'm always picking at something on Opal, with an eye towards improving efficiency.
Current activities involve addressing efficiency concerns of the most common operations on paths.
Available through Virginia Tech library collection of ETDs. Projective Resolutions There has been an evolution of projective resolution algorithms for right modules over path algebras over the last several years. I have been working with Ed to translate the rough algorithm into something that can be implemented in Opal. The algorithm exploits the relationship between the map structure and the underlying graph of the path algebra, and as a result is fast. Completion A fact of life when working in noncommutative algebras is that a Groebner basis, something that is needed for most computations we are interested in, can be infinite.