Assistant Professor of Mathematics Courtney Gibbons spent a week at the Mathematical Sciences Research Institute developing code for the computer algebra system Macaulay 2. Researchers in commutative and homological algebra have relied on Macaulay 2 to calculate examples and test conjectures for over two decades. Now Gibbons is one of a small group working to expand the program's functionality to noncommutative settings.
The package Gibbons is coauthoring will compute free resolutions and cohomology of ideals and modules over noncommutative rings. These constructions are important to mathematicians but also to modern physicists. In particular, Gibbons contributed an algorithm for computing Betti diagrams of such modules, which is a helpful first step for generalizing her own work on Betti diagrams to the noncommutative setting.
Interested nonspecialists can try out Macaulay 2 here.
