On Tue, Jan 6, 2015 at 9:40 AM, Peter Bruin <[email protected]> wrote: > Hi Jeroen, > > PARI now (as of somewhere in the 2.8 development branch) has a nfsplitting() > function to find the splitting field of a polynomial over QQ (i.e. the > Galois closure of an absolute number field). It does not yet exist for > relative number fields, as far as I can see. > > 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.). > 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 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. > 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? > > Peter > > > Op dinsdag 6 januari 2015 18:19:08 UTC+1 schreef Jeroen Demeyer: >> >> Hello, >> >> I will go the PARI workshop in Bordeaux next week and I will give a talk >> about "PARI and Sage". The PARI developers in particular want to know if >> Sage has any requests for PARI, things that we would like to be >> implemented in PARI. >> >> I can think of: >> >> * Porting Simon's 2-descent scripts to PARI >> * Splitting field/Galois closure (I have implemented this in Sage, but a >> native PARI implementation would make sense) >> * polgalois() in higher degrees; relative polgalois() >> * Factoring as generator function > > -- > 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 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. -- William Stein Professor of Mathematics University of Washington http://wstein.org -- 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.
