On Thu, Feb 14, 2008 at 2:07 PM, Andrew Mathas <[EMAIL PROTECTED]> wrote: > Hi Bill, > > Thanks for your reply. There are a couple of different ways to compute > the polynomials that I am interested in but they all fit the general > algorithm of computing a basis of Z[x,x^-1]-module and then recursively > stripping off "lower terms" so as to get a Z[x]-basis with certain nice > properties. The polynomials that I need are the coefficients of this > final basis when it is written as a linear combination of the "natural > basis" for this module. These polynomials can be quite complicated: any > polynomial in 1+N[x] or xN[x] can arise! However, the polynomials appear > to "grow" very slowly---actually, I have never seen anything on the > asymptotics of these polynomials, but heuristically this seems to be true. > > In gap3 I have some code for computing these things but I wrote this > code just for looking at "small" examples and I now want to compute all > of these polynomials which correspond to the "blocks of weight 4" for > the symmetric groups. The final polynomials that you get are all of > degree at most 4, and there really aren't that many different > polynomials that arise, but to get them I need to compute in some very > large symmetric groups and gap3 does not have enough memory to finish > the calculation which, as I have implemented it, is highly recursive > (all known algorithms are recursive, but some more than others). > > For my first project in sage I want to implement a less recursive > algorithm for computing these polynomials which will be more efficient > when computing them for a single "block" of a large symmetric group. The > basic algorithm is quite simple but I will need to rewrite a lot of > supporting code form gap in sage to set up the calculation. By the end > of this a fair proportion of the current (unreleased) version of my gap > share package will have migrated to sage (in a new and hopefully > improved form). > > So there is a point to this soliloquy. I have two questions: > 1. If I import FLINT will your code be automatically used by > LaurentSeries()?
No, not at present. We could change this with some work, which I think should really happen soon. > 2. I am currently thinking of writing the main part of the calculation > of these polynomials in cython. Is there is any real advantage in doing > this given how highly optimized FLINT already is. [The main routine here I would write the first version in Python then profile it and rewrite the parts that can get a speed boost in Cython. > will be a large loop doing something like a q-analogue of the Garnir > relations for the symmetric groups followed by stripping off lower > terms. I'll probably also rewrite functions like PartitionTuples() in > cython as this is very slow for large r and n in gap, and sage currently > calls gap for this function.] That would also be a great first submission to Sage. :-) William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
