John Cremona on Fri, 14 Feb 2014 13:59:15 +0100

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Re: ellnonsingularmultiple ?

The definition is clear to me!

I use the term "Tamagawa exponent" for n = lcm of the exponents of the
component groups, i.e. n such that n*P has good reduction at all
primes;  this is almost the same as the lcm of the Tamagawa numbers,
not quite because there's one case where the component group is C2xC2
so has exponent 2 but order 4.

Your n is more refined since it is specific to the point P.  It is the
lcm of the exact orders of P in the component groups at all primes p,
so if you were only returning n then I would suggest a name like
ellcomponent order.  But your name is OK, I think, given that pari
function names are not the prettiest anyway.....


On 14 February 2014 12:42, Karim Belabas
<> wrote:
> Hi pari-dev,
>   I just implemented a function that takes as input an elliptic curve E/Q
> (more precisely, a model defined over Q of a curve) and a rational point
> P in E(Q), and returns the pair [R,n], where
>   n is the least positive integer such that R := [n]P has good reduction at
>   every prime. More precisely, its image in a minimal model is everywhere
>   non-singular.
> (This is needed in our implementation of Bernadette Perrin-Riou's
> algorithms for p-adic heights.)
> 1) Is the above definition clear ?
> 2) What would be a good GP name for that function ?
>   [R,n] = ellnonsingularmultiple(E, P)
> is tolerable, but has anyone a better idea ?
> 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
> F-33405 Talence (France)  [PARI/GP]
> `