On 2014-04-07, Oren Becker <oren.bec...@gmail.com> wrote:
> My steps created matrices. The group PGL is implemented as a group of 
> permutations.
>
> I can make my question more accurate:
>
> I have a (symmetric) set of 2x2 matrices S over Fq. How can I find the 
> spectrum of the Cayley graph of PGL(2,q) with respect to the set of 
> generators S?

this is easy to do in GAP using the GRAPE package (part of
gap_packages spkg)

Use GAP's functionality to convert GL into PGL (you can make GL act on
lines, as a permutation group), then call CayleyGraph.


(you then can import the resulting graph into Sage using the interface
with GAP and compute the eigenvalues)

Should you need more details to implement this plan, 
please ask...

HTH,
Dmitrii


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