Software

Below are links to software that I have written or contributed to.  Some are no longer being maintained; for those, use at your own risk (but if you are interested in resurrecting it, let me know!)

Macaulay2 Packages

AssociativeAlgebras

This package (and its associated engine code) allows one to perform computations with noncommutative algebras in Macaulay2.  It is primarily designed for computations with connected graded algebras defined over a field.  It includes almost all computations that were once available in the NCAlgebra package.  It is currently maintained by myself is still in active development.  The most recent version is distributed with the Macaulay2 system.

DGAlgebras

This package allows one to perform computations with certain differential graded (DG) algebras and modules.  Computations include computing the algebra structure of the Koszul homology algebra of a ring, trivial Massey operations, Massey triple products, acyclic closures, and other similar computations.  It is currently maintained by myself and is still in active development.  The most recent version is distributed with the Macaulay2 system.

NCAlgebra

This package was written with Andy Conner.  It allowed one to perform computations with noncommutative algebras in Macaulay2.  However, all Gröbner basis computations are passed off to (and require the install of) the computer algebra system Bergman.  However, Bergman is no longer being supported (as you can see, the previous link is now dead!), so this system has been shuttered with AssociativeAlgebras above taking its place.  While the NCAlgebra package is still distributed with Macaulay2, it is no longer under development.

HopfAlgebras

This package was written with Colin Martin and Dakota White as part of each of their Master's Theses.  It allows for some computations with Hopf Algebras, with the primary emphasis being on finite-dimensional semi-simple Hopf algebras.  Hopf actions on noncommutative rings, as well as their invariants are also implemented.  This package uses NCAlgebra data types (see above) and as such is no longer in active development.  However, I hope to port the code to the new AssociativeAlgebra system soon.  I include the code here just in case someone would care to use it or try this themselves.

Other Software

PolynomialAlgebras

This is a software package written in Haskell that explores how a functional language may be used to implement polynomials.  It is the main "deliverable" appearing in the Master's Thesis of my student Tommy Meek.  Of particular interest are the presence of type-level (dense and sparse) monomials as well as a functional implementation of multivariate polynomial long division as well as Buchberger's algorithm.