Re: ellwp over fields which are not t_REAL or t_COMPLEX

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Jeroen Demeyer [2014-02-24 13:59]:
> Both these used to work in PARI-2.5.5 but no longer work in
> PARI-2.6.2. Is this a bug or was ellwp() never intended to work for
> these fields?
> 
> gp> ellwp(ellinit([0,0,0,Mod(1,1009),0]))
>   ***   at top-level: ellwp(ellinit([0,0,0
>   ***                 ^--------------------
>   *** ellwp: incorrect type in roots (t_INTMOD).
> gp> ellwp(ellinit([0,0,0,Mod(x,x^2+5),0]))
>   ***   at top-level: ellwp(ellinit([0,0,0
>   ***                 ^--------------------
>   *** ellwp: incorrect type in roots (t_POLMOD).

This was an oversight. I'm not too fond of the ellwp (and ellsigma /
ellzeta) interface :-(

In fact those are elliptic *functions*, and only remotely related to
elliptic curves. One normally associates them to
- a rank-2 lattice in C
- or a pair of elliptic invariants (g2,g3)   [ N.B. there's no GP
  interface for this ]

The rule chosen to associate them to elliptic curves defined over C was
via the period lattice E.omega. But E.c4/E.c6 equally give us elliptic
invariants (up to renormalization), and this makes no asumption about
the base field being C... For some reason, this had disappeared in 2.6.0

Now fixed in master.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
`