Re: ellap: I can't reproduce example from manual

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

* Shevek [2018-03-03 10:33]:
> I'm trying to understand the use of 'ellap' to compute the Frobenius
> trace of elliptic curves defined over different fields.
> 
> Then I stucked on an example verbatim taken from the manual (*):
> 
> ---------------------
> ? Fq = ffgen(ffinit(11,3), 'a); \\ defines Fq := F11^3
> ? E = ellinit([a+1,a], Fq);  \\ y^2 = x^3 + (a+1)x + a, defined over Fq
> ? ellap(E)
>   ***   at top-level: ellap(E)
>   ***                 ^--------
>   *** ellap: incorrect type in ellap [can't determine p] (t_VEC).
>   ***   Break loop: type 'break' to go back to GP prompt
> ---------------------
> 
> What is wrong here? The example was played on versions 2.9.3 (self
> compiled) and 2.7.5 (from Ubuntu package). The system is Ubuntu 16.04

There's a typo in the manual, sorry.

The correct syntax is

  a = ffgen(ffinit(11,3), 'a);
  E = ellinit([a+1,a]);
  ellap(E)

Cheers,

    K.B.

P.S. Or, if you want to be really explicit :
  a = ffgen(ffinit(11,3), 'a);
  E = ellinit([a+1,a], a);
  ellap(E)

I.e. our convention is that any finite field element built from the
ffgen constructor may be used to specify that finite field. Just
writing 'a' by itself without having previously assigned a finite field
element to it yields a polynomial in Q[a], not what you wanted.

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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