On Wed, 07 Feb 2007 08:57:09 -0700, Kiran S. Kedlaya <[EMAIL PROTECTED]> wrote: > There's a question below about availability of some features in SAGE, > which we may need for my AWS project.
Thanks. There's definitely going to be some basic things that are not in any free software that you'll have to implement. > - -------- Original Message -------- > Subject: Re: AWS project > Date: Wed, 7 Feb 2007 10:38:00 +0100 > From: Ralf Gerkmann > To: [EMAIL PROTECTED] > References: <[EMAIL PROTECTED]> > <[EMAIL PROTECTED]> > <[EMAIL PROTECTED]> > > > When I searched the SAGE manual for features that we > could probably use for the project, I have noticed that > some essential functions are still missing. > > - - multivariate polynomials: > given an ideal I = (f_1,...,f_r) and some g in I, find s_1,...,s_r such > that g = s_1 f_1 + ... + s_r f_r (this doesn't seem to be available > even for Groebner basis) You're right that this doesn't seem to be available, which is a strange oversight. It *must* be easily available within Singular though, so it's probably a few lines of code to add it to SAGE. > - - padic rings: > Hensel lifting of finite field elements and factors of polynomials > over finite fields Polynomial factorization over finite fields is in SAGE. There is also a factor_pdic method on polynomials over QQ. I don't think Hensel lifting is available in general though. > As far as I have seen, no algebraic extensions of padic rationals > are available so far. However, they can easily be constructed > as quotients of polynomial rings. Maybe unramified extensions > would be enough for our purposes. In order to construct extensions > whose generator is a Teichmueller lift we would need Hensel lifting. > We also need an implementation of the Frobenius action on the > unramified extension. You're right, extensions of Qp are not implemented, except as quotients of polynomial rings. Moreover, Qp itself is implemented poorly in SAGE, at least regarding how fast it is. It is one of the few rings for which (1) nobody seems to have ever written a good free C or C++ library to compute in it, and (2) its unclear what the right semantics are, so improvement of it has been more difficult than for most other rings in SAGE. > I guess it wouldn't be a big deal for me to implement these > functions, including a mini-class called "LocalField" or > similarly. Or do you know that these functions are already > available somewhere else? See above. Definitely creating a *mini* Local Field class would be a good idea. -- William > > Ralf > -----BEGIN PGP SIGNATURE----- > Version: GnuPG v1.4.2.2 (GNU/Linux) > Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org > > iD8DBQFFyfbVgT1c97rJjv0RAgJUAJ43gBGlC9NFiLUm9uuvnOgfHax9HgCfZYnO > 3iCjcJTl4glXVSdq/5B13rI= > =/aGY > -----END PGP SIGNATURE----- > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
