On May 30, 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)?
I think so, but I don't know how good latex2html is at this sort of
thing. I should try adding some into the plotting sections...
> 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.
Well, anyway, I have a draft of the tutorial in which the "Guided
Tour" has been revised pretty substantially.
<http://trac.sagemath.org/sage_trac/ticket/3347>
Any comments would be helpful.
I haven't even thought about writing up your two ideas; at this point,
though, I feel more comfortable editing existing text than trying to
add new sections like this.
> 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
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