Dear Rudi, Generating nonbases hypergraph that contains the Aut(M) is clear.But what i'm not clear is how do i verify if the Automorphism group of the above constructed graph is generated by the automorphism group of the matroid?
Can you provide some thoughts on this. Thanks On Wed, Mar 5, 2014 at 4:15 AM, Pendavingh, R.A. <[email protected]>wrote: > Dear Rajesh, > > Please call me Rudi. > > As far as i can see,the magic numbers are calculated for each reduced > matrix, displaying each basis. > OK, thanks. > > > Regarding, the automorphism group of a matroid, we should certainly avoid > the full non-bases calculation.Can you please suggest some resource,( if > you have something particular in mind ), for studying the hypergraphs that > are invariants of a matroid? > > I did not have a particular reference in mind. What I was thinking of as a > first attempt was, say, the hypergraph whose edges are all the flats of > rank k, taking O(n^k) time. That particular hypergraph I expect to work > well for linear matroids over small fields, also assuming that the rank of > these matroid is not too big compared to k. But which hypergraph to try > will always depend on the representation of the matroid. > > I am not sure about the BasisMatroid. Here the construction of the > nonbasis hypergraph is relatively inexpensive compared to the size of the > representation, and it seems difficult to come up with any hypergraph that > is faster to compute. But it may still give a speedup to avoid the > construction. I actually have a routine implemented that inspects the > nonbasis hypergraph without constructing it (running through the r-sets), > and which calculates, for each element e, the number of nonbases containing > e. Coloring the groundset elements with this information may cut down the > isomorphism group significantly, since all automorphism must preserve > color. You get this partition by calling M._basis_partition() on a > BasisMatroid. If you get a partition into singletons, the automorphism > group is clearly trivial, and perhaps other outcomes may also be exploited > for a speedup. Also, check out M._basis_partition2(). This does create the > nonbasis hypergraph as a SetSystem, but then finds an equitable partition > for it. In the course of that computation, a trimmed version of the > nonbasis hypergraph is created. This seems a better object to feed to the > graph automorphism group computation, since it's much smaller. > > I'm also reading your paper<http://arxiv.org/pdf/1203.0910v2.pdf> for > understanding the projective invariants of matrices. > > Let me know when something needs clarification. It is a technical story. > > Best, > Rudi > -- *Rajesh Veeranki** | Senior Undergraduate | **C.S.E** | **IIT Bombay* -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-gsoc. For more options, visit https://groups.google.com/d/optout.
