Re: idealstar

["John Cremona" <john.cremona@gmail.com>]

Thanks, that is exactly what I was looking for.

John

2008/12/2 Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>:
> * John Cremona [2008-12-02 18:27]:
>> Dear pari,
>>
>> The function idealstar(k,I) for an ideal I in a number field k,
>> returns an abstract representation of the group (Z_K/I) together with
>> generators.  using this I can easily form the map from the abstract
>> group to the concrete one, but what about the inverse?  In other
>> words, given an element of Z_K coprime to I, how can I express it in
>> terms of the abstract generators?  is there a function for this, or
>> has someone else implemented it?
>>
>> I fully realise that one special case of this is the discrete log
>> problem for Z/pZ, and am not asking for anything which is very fast,
>> but I hope I will not have to kist all the lements and check them one
>> by one.
>
> (18:30) gp > ???"discrete log"
> bnfisprincipal elllog         fflog          ideallist      ideallog
> idealstar      znlog
>
> I'd have a look at "ideallog" ...
>
> As you mentionned, the bottleneck is the computation of discrete logs in
> (Z_K / P) for maximal ideals P dividing I. This will be slow if Norm P - 1
> is not smooth ( basic Pohlig-Hellman + Shanks ).
>
> 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
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>