Re: adding orders?

[Denis Simon <denis.simon@unicaen.fr>]

Hi,

I vote for nforder(T,arg) which seems good.

Denis SIMON.

----- Mail original -----
> De: "Karim Belabas" <Karim.Belabas@math.u-bordeaux.fr>
> À: "Aurel Page" <aurel.page@normalesup.org>
> Cc: "pari-users" <pari-users@pari.math.u-bordeaux.fr>
> Envoyé: Dimanche 17 Juin 2018 22:53:23
> Objet: Re: adding orders?

> Now that I think of it, my suggestion was stupid : we can't have an 'nf'
> as a first arguement since the function will be mostly used in case
> the maximal order is not computable.
> 
> So the only sensible interface I can thing of is something like nforder(T, v)
> where  T is a monic polynomial in Z[X] and v is a vector of elements in
> Q[X] / (T)  [ t_INT or t_FRAC or t_POL or t_POLMOD mod T... ]
> 
> It would return a matrix in HNF (say) for the order
> Z[v[1], ..., v[k]] in terms of the power basis of Z[X]/(T). [ With rational
> coefficients of course. ]
> 
> But since it's indeed useful to adjoin elements to an existing order,
> we can allow square t_MAT as well as elements of v [ representing orders
> as per the previous convention...].
> 
> It would be mostly useless in library mode (already exists and hardcoded
> in a few places), but it's nice to export it for GP use.
> 
> Cheers,
> 
>    K.B.
> 
> * Aurel Page [2018-06-17 22:38]:
>> Hi,
>> 
>> Why not a single argument, which can be a t_VEC for several elements? One
>> might want an order generated by more than two elements. Or 'a' itself can
>> be an order?
>> For the name, "nfordergenerated" would be accurate but a bit too long :-(
>> 
>> Cheers,
>> Aurel
>> 
>> On 17/06/18 22:31, Karim Belabas wrote:
>> > * Bill Allombert [2018-06-17 20:59]:
>> > > On Wed, Jun 13, 2018 at 02:41:46PM +0100, J E Cremona wrote:
>> > > > Is there a pari or gp function to add two orders in a number field?  Here
>> > > > of course I mean to return the smallest order containing both the summands,
>> > > > not just their sum as Z-modules, so the sum of Z[a] and Z[b] would Z[a,b].
>> > > I do not think this is readily available, though it is probably
>> > > done inside nfmaxord.
>> > > Do you have an algorithm for this task ?
>> > It's mostly available (internally). What would be a suitable name ?
>> > nforderadd ? (not too fond of that one...). Maybe, just nforder(nf, a, {b}) ?
>> > (cf idealhnf(nf, a, {b}).
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
> 351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
> `