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)? 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 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. -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 --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
