On Thu, Mar 26, 2015 at 2:04 PM, Daniel Nichols <[email protected]> wrote: > Hi everyone, > > I'm a mathematics PhD student at the University of Massachusetts, and I'm > looking for an interesting project to work on this summer. My field is > computational number theory. I'm really interested in the GSoC 2015 project > concerning Hermite normal form for modules over Dedekind domains. I have > Cohen's book and I've been reading about the algorithm. I know applications > are due tomorrow, but I still wanted to introduce myself here before > submitting. > > I hope there might still be enough time for me to ask for a small > clarification about the goals of the project. I did some looking around and > it looks like PARI's function nfhnf, which finds an HNF pseudo-basis for a > module given by a pseudo-matrix, is already wrapped in SAGE as of 2013. See > the Sage documentation -- there's even an example here where the base number > field is not a PID. > > Is the desired HNF functionality mentioned in the project synopsis different > from this?
No, it's that. But the wrapping is not sufficient, e.g., it needs to be actually used to do computations with finitely generated modules over the ring of integers of a number field. > PARI has another function, rnfhnfbasis, that is specifically for > modules over relative number fields. Maybe this is the function that needs > to be wrapped? No. > > I saw in another thread here that the conclusion from last summer's tests > was that PARI's HNF functions might be too slow and buggy to be wrapped for > inclusion in Sage. If that's the case, I would still be very interested in > working on this project and writing something new directly in Sage rather > than wrapping PARI. Yes, definitely. We want an HNF that is (at least) as fast as Magma's, especially when the input is a dense matrix with large entries (but not necessarily very many rows and columns). One motivating application is arithmetic with quaternion algebras defined over number fields. William > > Thanks very much, > > Dan > > -- > You received this message because you are subscribed to the Google Groups > "sage-gsoc" 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-gsoc. > For more options, visit https://groups.google.com/d/optout. -- William (http://wstein.org) -- You received this message because you are subscribed to the Google Groups "sage-gsoc" 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-gsoc. For more options, visit https://groups.google.com/d/optout.
