I think this this can be done. The parts David Loeffler and I have contributed separately could be merged into something more coherent structure ... . It would be good if the people interested in this topic could meet at some point in time - this would be probably most efficient.
In my view view the whole arithmetic subgroup part of sage needs to be put into a more coherent and efficient structure. In addition there is, as as Georg Weber pointed out, a way to get rid of one loop in the search algorithm for the pairing. This only works for the congruence subgroups, but would make the algorithm for the Farey symbols O(index) as opposed to O(index^2). This is particularly useful for the Gamma(n) for large n. We are already much faster than Magma but with this improvement the algorithm would be as good as it gets. My view on this is that the last point is the most urgent currently (the string theory guys would like that part). In addition I have collected a number of minor improvements to the Farey symbols and the arithmetic subgroups which I would like to add at some point in time. Am Samstag, 21. Juli 2012 19:20:50 UTC-6 schrieb vdelecroix: > > Hello, > > There is a nice code for computing Farey symbols of arithmetic groups > (see [1] and [2]). My question is about implementation. There are > basically two ways of describing a subgroup of SL(2,Z). Either by > providing a membership test (ie a __contains__ method) or by giving a > Shreier graph for some system of generators. The former implementation > is used for congruence subgroups while the latter provides a way to > describe any arithmetic group (see > sage.modular.arithgroup.arithgroup_perm). > > The current implementation of Farey symbols relies on membership test > which costs a lot for a group given by its Shreier graph (we first > decompose the matrix in standard generators of SL(2,Z) via continued > fraction and then test if the word is a loop in the Shreier graph). My > question is whether it is possible to adapt the current implementation > of the computation of Farey symbols to the case of a group given by > its Shreier graph ? > > Best, > Vincent > > [1] http://trac.sagemath.org/sage_trac/ticket/11709 > [2] http://trac.sagemath.org/sage_trac/ticket/11875 > -- -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
