Hi William, Op dinsdag 6 januari 2015 19:19:30 UTC+1 schreef William stein: > > On Tue, Jan 6, 2015 at 9:40 AM, Peter Bruin <[email protected] > <javascript:>> wrote: > > > > What exactly do you mean by "factoring as a generator function"? > > > > One thing people often request for Sage is the ability to do something > like this: > > sage: > add_known_prime(23368017336614295144112598516264902899420576615151) > > and then whenever you do anything that might involving factoring > integer, Sage would first do trial division by known primes. To > implement this properly, it would be by far best to do it at the level > of PARI, so that's pari's internal factor function respects the list > of known primes, and uses it everywhere (e.g., when computing a > maximal order, etc.). > PARI has functions addprimes() and removeprimes() to manipulate the list of known primes, but these are currently not used by Sage.
> I am also going to the PARI workshop and am planning to try to understand > > the modular symbols functionality. I am mostly interested in this for > its > > own sake, but it would also be interesting to wrap this code in Sage as > an > > alternative to the existing Sage implementation of modular symbols. > > I wasn't aware of that. A quick Google search finds these slides from a > talk: > > http://pari.math.u-bordeaux1.fr/Events/PARI2014/talks/modsym.pdf > It is fairly recent; Karim Belabas and Bernadette Perrin-Riou have been working on this on and off for some time, and Karim merged this into the development version of PARI last June. The biggest challenge, IMHO, with implementing modular symbols in pari > for anything but toy problems -- at least in the past -- was that none > of their linear algebra algorithms were (1) asymptotically fast, or > (2) leveraged sparse matrix algorithms. But maybe this package > changes that. > The PARI implementation seems to use somewhat different techniques than Sage; apparently it uses less linear algebra but follows ideas from a paper of Pollack and Stevens cited in the PARI source (basemath/modsym.py): Pollack and Stevens, Overconvergent modular symbols and p-adic L-functions Annales scientifiques de l'ENS 44, fascicule 1 (2011), 1-42 http://math.bu.edu/people/rpollack/Papers/Overconvergent_modular_symbols_and_padic_Lfunctions.pdf and is (at least partially) adapted from a Magma package by Darmon and Pollack: Darmon and Pollack, Stark-Heegner points via overconvergent modular symbols http://www.math.mcgill.ca/darmon/programs/shp/shp.html > Apart from that, I want to try to improve linear algebra (mostly over > finite > > fields) in PARI. Not sure if this is immediately useful for Sage, but > it > > could be. > > Are there any options to link FLINT to PARI yet, which would provide a > shortcut approach to that problem? > Unfortunately not, and I don't think the PARI developers have such plans. For some computations having to do with my research (which heavily rely on linear algebra over finite fields), I have considered various mixes of FLINT, PARI and Sage. Using just PARI gives the right balance between developer time and running time for me at the moment. An alternative to speeding up linear algebra in PARI (my current plan) would be to rewrite much of my own code to use FLINT, but I guess working on linear algebra in PARI is more useful generally speaking. Peter -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
