Hi William,

Looks great. If the last talk got me in the mood to work, this one has
me incredibly fired up! :)

Some minor corrections:

page 5: upper triangule -> upper triangular
page 21: Mestra -> Mestre
page 21: another modular X -> another module X (or possibly a different wording)
page 21: only interested in -> only interesting in
page 24: I'm curious about that VM basis timing -- what machine did
you run it on? FWIW, I've also rewritten the code (which I have yet to
submit), for a pretty serious speedup. These times are on my laptop,
where the "xxx_" version is the new code:

sage: time B = victor_miller_basis(200, 18)
CPU times: user 0.46 s, sys: 0.01 s, total: 0.47 s
Wall time: 0.51 s

sage: time B = sage.modular.modform.vm_basis.xxx_victor_miller_basis(200, 18)
CPU times: user 0.03 s, sys: 0.01 s, total: 0.03 s
Wall time: 0.05 s

sage: time B = victor_miller_basis(200, 180)
CPU times: user 45.92 s, sys: 1.53 s, total: 47.45 s
Wall time: 50.94 s

sage: time B = sage.modular.modform.vm_basis.xxx_victor_miller_basis(200, 180)
CPU times: user 0.19 s, sys: 0.05 s, total: 0.25 s
Wall time: 0.26 s

I'll clean those up and submit them soon, since I need them for
something I'm working on ... I'm currently in the process of making
spaces of modular forms of level one subclass the existing code, and
actually take advantage of all our fast E_k and Delta computation
code, as well as cleaning things up a bit.

p. 34: It's -> Its, and that sentence should be reworded: "J_1(N) has
a canonical model of abelian variety" could maybe become "a canonical
model which gives it the structure of an abelian variety", or
something along those lines.
p. 34: annd -> and
p. 35: The title reads strangely; maybe "Defining Modular Abelian
Varieties in Sage"?


-cc

On Thu, Oct 16, 2008 at 4:18 PM, William Stein <[EMAIL PROTECTED]> wrote:
> Hi,
>
> My last talk at Bordeaux is tomorrow morning (in 7 hours) on modular forms.
> See the attached slides or Sage notebook file.
>
> Note that I view the "slide version" of this talk exists really only
> for the talk I'm
> giving tomorrow.   The sage notebook and a normal article (or new section
> for the Sage documentation that will be in ReST) or the real format in which
> this talk will live longterm...
>
>  -- William
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washington
> http://wstein.org
>
> >
>

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