I have a {0,1}, invertible, triangular matrix, that I would like to show is totally unimodular. Are there any known results on the total unimodularity of classes of triangular matrices?



When is a triangular matrix totally unimodular?
[Seymour's decomposition theorem](http://en.wikipedia.org/wiki/Matroid#Regular_matroids) for regular matroids yields a polynomial-time algorithm for testing if any {0,1,-1} matrix is totally unimodular. Unfortunately, due to the sound of paint drying on this [question](https://mathoverflow.net/questions/27346/has-anyone-implemented-a-recognition-algorithm-for-totally-unimodular-matrices) of Gordon Royle, it seems as if no one has yet implemented it. 


