Karim Belabas on Fri, 07 Aug 2015 09:37:15 +0200 |
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Re: elllocalred vs. ellglobalred |
* John Cremona [2015-08-06 16:43]: > On 6 August 2015 at 14:11, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr > > wrote: > > > On Thu, Aug 06, 2015 at 01:13:30PM +0100, John Cremona wrote: > > > For E and elliptic curve over Q, the 3rd component of elllocalred(E,p) > > is > > > the [u,r,s,t]-transformation required to take E to a local minimal model > > at > > > p. The 5th component of ellglobalred(E) is supposed to be a list all the > > > elllocalred(E,p) for all bad primes; but in the output of > > > ellglobalred(E)[5] all the 3rd components are 0! > > > > The documentation says: > > > > * L is a vector, whose i-th entry contains the local data at the i-th > > prime > > divisor of N, i.e. L[i] = elllocalred(E,F[i,1]), where the local > > coordinate change has been deleted, and replaced by a 0. > > > > > In my version it is different: > > ?ellglobalred > ellglobalred(E): E being an elliptic curve, returns [N,[u,r,s,t],c, faN,L], > where N is the conductor of E, [u,r,s,t] leads to the standard > model for E, c is the product of the local Tamagawa numbers c_p, faN is > factor(N) and L[i] is elllocalred(E, faN[i,1]). Well, Bill quoted the extended help (??ellglobalred), which has been correctly updated, whereas the basic help (?ellglobalred) has not. :-( I'm fixing that. > so this must have changed. Indeed, about 2 years ago : in commits 35191d80, e98a75c6, c280f9e6. I "discovered" the (global) Laska/Kraus/Connell algorithm at that time [ for which I later found a better presentation in your book ! ] and used it to rewrite ellminimalmodel so that it skipped Tate's local algorithm (elllocalred, which gives more information, of course). As a result, the operation became quite inexpensive, and allowed to fix in a cheaper way the (very annoying, albeit documented) bug that many functions gave wrong results on non minimal inputs. So I rewrote all local tests in terms of Kraus's criterion. As a side effect of these minimality-related rewrites, I decided to delete the (redundant) information from the ellglobalred output. And forgot to update the basic help. Cheers, K.B. -- Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17 Universite de Bordeaux Fax: (+33) (0)5 40 00 69 50 351, cours de la Liberation http://www.math.u-bordeaux.fr/~kbelabas/ F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP] `