Equivalence-free exhaustive generation of matroid representations

In this paper we present an algorithm for the problem of exhaustive equivalence-free generation of 3-connected matroids which are represented by a matrix over some finite (partial) field, and which contain a given minor. The nature of this problem is exponential, and it appears to be much harder than, say, isomorph-free generation of graphs. Still, our algorithm is very suitable for practical use, and it has been successfully implemented in our matroid computing package MACEK [http://www.mcs.vuw.ac.nz/research/macek, 2001–05].