John Cremona on Fri, 14 Feb 2014 13:59:15 +0100 |
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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..... John On 14 February 2014 12:42, Karim Belabas <Karim.Belabas@math.u-bordeaux.fr> 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 http://www.math.u-bordeaux1.fr/~kbelabas/ > F-33405 Talence (France) http://pari.math.u-bordeaux1.fr/ [PARI/GP] > ` >