Re: adding orders?

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

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]
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