A Macaulay2 package for computing with ordered matroids
While writing my thesis at the UPC in Barcelona I wrote a number of scripts to facilitate computations with ordered matroids in Macaulay2 (M2), an open source computer algebra system available here. Sometime later I discovered Justin Chen’s Matroids package and decided to extend it to include methods for ordered matroids. The consequence of that decision is the package MatroidActivities, which is available freely here.
The new version of MatroidsActivities (0.2) has greatly increased functionality. One can still work compute external and internal orders (see here for definitions) and determine if a given ordered matroid is internally perfect. Moreover, one can now construct the broken-circuit complex and the Orlik-Solomon algebra of an ordered matroid. In addition to the new methods available for ordered matroids in Version 0.2, there are also a great deal more methods for unordered matroids. The crucial new constructions include the ability to construct a matroid from any of the following M2 types: ideals, hyperplane arrangements, and simplical complexes. One can also now test if a given matroid is (co)graphic, binary, ternary, regular, paving, or simple.
MatroidActivities is exhaustively documented so instead of giving a full run-down on what it can do, let me just encourage you to go download it here and give it a whirl. There is also an introductory session that walks through the basic methods available and computes some examples illustrating the usefulness of the package.
Please do get in touch if you have any questions, feature requests, and/or bug reports.