On Fri, May 30, 2008 at 6:44 PM, mhampton <[EMAIL PROTECTED]> wrote: > > Maybe they are better put in another place (Sage Constructions > perhaps), but I have some ideas for broadening the tutorial: > > 1) In calculus/differential equations, give a cythonized version of > Runge-Kutta, and maybe an @interact example on different numerical > methods; there are a couple of @interact things on the wiki that could > be chosen or combined for that. Is it possible to include screenshots > in the tutorial (.pngs)?
Yes, it should be. If it isn't we should fix that problem. > 2) The tutorial should have some simple stats examples, pretty early > on I think. I'm not sure what exactly to suggest though. Probably > better to use scipy.stats instead of R for pythonic continuity. I just spent the week talking about scipy.stats and R/rpy in my class. See http://wiki.wstein.org/2008/480a/schedule for pdfs and sws's for each day. There are some examples there. I talked a lot about scipy.stats actually. That system does a lot, but it also has a lot of room to improve. It's really usable though (very straightforward and systematic), and fairly well documented, and has *tons* of distributions built in. I would love to see some discussion about how people involved in Sage could improve scipy.stats. This would be *both* (1) something sage-specific that involves better integration into Sage (probably GPL'd), and (2) improvements in scipy.stats itself that would go back into scipy. For example, scipy.stats is all pure Python, hence pretty slow, and it has some basic bugs due to insufficient (unit and doc) testing. > I haven't chipped in yet at all on the documentation, but I'd like to > at some point. Realisitically, that might not be until next spring > when I am on leave. I'm glad to hear you'll be on leave so you can work on Sage more :-) > > -M. Hampton > > On May 30, 7:17 pm, "William Stein" <[EMAIL PROTECTED]> wrote: >> On Fri, May 30, 2008 at 4:33 PM, David Joyner <[EMAIL PROTECTED]> wrote: >> >> > On Fri, May 30, 2008 at 5:27 PM, John H Palmieri <[EMAIL PROTECTED]> wrote: >> >> >> I'm working on rewriting the tutorial. Section 2.5.1 of the tutorial >> >> is about Dirichlet characters, and I have some questions: >> >> >> The introductory sentence discusses "Dirichlet characters", and then >> >> the first example uses "DirichletGroup". What is the connection? >> >> (I'm thinking that for fixed n and R, the set of Dirichlet characters >> >> forms a group, and that's what's being computed here. Is that right? >> >> If so, in the notation for elements of the group, what function does >> >> an element like [1,zeta6] correspond to?) >> >> > As you suspected, the set of all Dirichlet characters mod N form a group >> > called the DirichletGroup. The notation [1,zeta6] might be distracting >> > for a beginner, as it is what I would call the SAGE internal representation >> > for a fixed generator chi of DirichletGroup(21). The ordering in which the >> > group elements are listed is (I think) as powers of the generator. >> > For example, the 11th element is the 11th power: >> >> > sage: G = DirichletGroup(21) >> > sage: len(G) >> > 12 >> > sage: chi1 = G.gens()[1] >> > sage: chi1 >> > [1, zeta6] >> > sage: chi2 = G[10] >> > sage: chi2 >> > [1, -zeta6 + 1] >> > sage: chi2(19) >> > zeta6 >> > sage: chi1(19)^11 >> > zeta6 >> > sage: chi1^11 >> > [1, -zeta6 + 1] >> > sage: chi1^11 == chi2 >> > True >> >> >> The introductory sentence also discusses "some ring" R. Is R actually >> >> the complex numbers here? Can we add a parenthetical remark like >> >> "(Often, R is the complex numbers.)"? >> >> > Yes this sounds good to me. >> >> No, the default is a cyclotomic number field. >> >> sage: DirichletGroup(13).base_ring() >> Cyclotomic Field of order 12 and degree 4 >> >> It's possible that Dirichlet characters are too specialized for the tutorial. >> It made a lot of sense when SAGE = "System for Arithmetic Geometry >> Experimentation", back when we first put together the tutorial. Now, >> I'm not so sure. >> >> Comments? >> >> >> >> >> The introductory sentence discusses a map with domain (Z/NZ)*. A bit >> >> later, a Galois group involving zeta_n is mentioned. Presumably n = >> >> N? >> >> > No. The group order of DirichletGroup(N) is the Euler totient \phi(N), >> > so with N=21, >> > n=12: >> >> > sage: euler_phi(21) >> > 12 >> >> Yes, since DirichletGroup(N) is isomorphic to the dual of (Z/NZ)^*, >> and dualizing twice gets back to to the original group. >> >> Anyway, I would love to have feedback about the topics >> covered in the tutorial. I think it would make good sense >> to revisit the choice of topics and "freshen it". Any volunteers >> or suggestions? >> >> -- William > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
