I can't seem to find a "standard" way to implement/manipulate matroids in Mathematica. (They do not seem to be included in Combinatorica, for instance, and googling has turned up nothing.) Ideally, it will be possible to work with bases (as e.g. Macaulay2 does), and to depict their basis exchange graphs. Is there a package for this which I've overlooked, and/or is there a typical way to do this "by hand"? Thank you.
