Hi Rajesh,

Welcome! Good to see you getting started with Sage development. What 
textbook do you use for your course? That could help pointing you in the 
right direction.

For the automorphism group, the way to go is to construct an appropriate 
graph (e.g. a bipartite one with the elements on one side, the non bases on 
the other, and an edge if the element is contained in the non basis), and 
compute the automorphism on that graph that preserves the sides of the 
bipartition.

For k-connectivity, the standard way is to iterate over all pairs (X,Y) of 
size-k subsets (so |X| = |Y| = k) that are disjoint, and compute the 
intersection of M/Y\X with M/X\Y. Hopefully your textbook has details.

Both of these are relatively small, warm-up projects. Efficient minor 
testing is a bigger fish, which will require a lot of tuning to get the 
algorithm right. You should probably start with binary matroids, and you 
can look to Hlineny's MACEK project for inspiration (I believe his manual, 
or one of his papers, has a few lines on how he does it. His code is a good 
benchmark for the speed we want). Rudi Pendavingh also may have some ideas 
here.

Cheers,

Stefan.



On Tuesday, February 25, 2014 12:13:42 PM UTC-5, Rajesh Veeranki wrote:
>
> Hi,
>
> This is Rajesh Veeranki,a final year B.Tech C.S.E student at IITB.I'm 
> excited about sage and want to contribute something to it.
> I'm comfortable with* Matroid theory*,as i'm doing a course in it.So that 
> would be my primary choice.I've got my hands dirty by working on some 
> tickets( 15000 <http://trac.sagemath.org/ticket/15500> , 
> 14667<http://trac.sagemath.org/ticket/14667>
>  )
>
> As far as the project is concerned, can the mentors please suggest some 
> resources relevant to it ( such as testing connectivity,efficient minor 
> testing or automorphism group computation), that helps me in making a good 
> application.
>
> Looking forward to working with sage.
>
> Thanks!
>
> -- 
>
>
> *Rajesh Veeranki** | Senior Undergraduate | **C.S.E** | **IIT Bombay* 
>
>  

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