Andreas Enge on Wed, 15 Feb 2012 19:04:14 +0100

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Re: Elliptic modular functions

On Wed, Feb 15, 2012 at 06:27:27PM +0100, Karim Belabas wrote:
> eta(x, 1) ?
> These are exported as weber(x, 0 / 1 / 2)

Ah, sorry! I had been looking for them under "ell...", together with ellj and
ellsigma. (And even got side tracked by elleta, but which is the other one.) Would
it make sense to rename them with a common prefix such as "mod"? Or add "ell"
to all of them?

> > ellgamma2, ellgamma3.
> I'm not sure what these two denote: maybe elleisnum(E, 2 / 3, 1)  ???

No, j^1/3 and (j-1728)^1/2, respectively. Both occur as class invariants, and
the main interest of the former is that j=gamma2^3 is a good computational
definition of j.

> So it seems they are all already exported. It would be interesting to
> test and optimize them, though...

Okay; but this is even less urgent then, since our students can already
start using the existing functions. Thanks for the pointers!