Re: Component [5] of prime ideal structure

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

* Jeroen Demeyer [2014-02-11 11:34]:
> gp> idealprimedec(nfinit(x^2+1), 5)[1][5]
> %4 =
> [2 -1]
> 
> [1  2]
> 
> What is the meaning of this?

This is the multiplication table by the anti-uniformizer b. If mb := pr[5],
then mb[,1] is the old value ( = b * nf.zk[1] = b )

> The documentation ??idealprimedec says
> that it is supposed to be an algebraic integer, but I don't
> understand
> it. This changed from PARI-2.5 to PARI-2.6 and it breaks Denis
> Simon's GP scripts.

This was mentionned in CHANGES-C.27, but not in 'COMPAT', and
??idealprimedec had become inaccurate. I just fixed all that.

If I understand correctly, the only reason this was needed in Denis's
scripts is that we do not export the ZC_nfvalrem function that returns
both the valuation *and* the part coprime to the prime ideal.

The nfval()  function (and the valuation() function for that matter)
should take an extra optional argument to return that coprime part.

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]
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