Re: Pari Bug?

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

* John Cremona [2004-06-28 18:44]:
> It is very likely that elllseries only gives correct answers with a 
> global minimal model.  This is true, though not always documented, with 
> several of Pari's elliptic curve functions.

I'd appreciate a list of problematic routines you are aware of, besides the
documented ones, which are

  ellak
  ellan
  ellap
  ellbil
  ellheight
  ellheightmatrix
  elllseries
  elltaniyama

[ I'm talking about the unstable branch, which everybody should consider
using nowadays ]

> So you will ask -- why does elllsseries not switch to a minimal model 
> itself?  I suppose the answer is that this would only waste time when 
> the curve was minimal already.

Exactly.

> A solution would be to do this unless the user has set a switch/flag to
> say "don't bother minimising this  model as I already know that it is
> minimal".

It would certainly be as complicated for the user to set such a flag,
than to simply start her computation with 

  e = ellminimalmodel(e);

And introducing consistently such flags would quite a bit complicate the
PARI code and calling interfaces.

The PARI philosophy requires the user to do all relevant initialisations on
her own first. It sometimes requires careful reading of the documentation,
but I think it is the best approach.

    Karim.

P.S: In the case at hand, it is true that in concrete cases, ensuring that
the model is minimal at all relevant primes can be done cheaply. But
performing extra initializations in all subroutines is bound to be
inefficient.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dep. de Mathematiques, Bat. 425   Fax: (+33) (0)1 69 15 60 19
Universite Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]