idealred in narrow sense

[Pierre.Charollois@math.u-bordeaux1.fr]

Dear Pari-Users ,


 Dealing with an ideal J in the narrow sense,
 I was trying to use  the "idealred" command to
 find an equivalent ideal in HNF form having smaller coefficients.


 Unfortunately, it seems that  "idealred" returns
 an equivalent ideal that can be in another narrow class.

 For instance, if you pick J to be one generator of the narrow class group,
 idealred sometimes returns the trivial matrix.

e.g.
(09:20) gp > K=bnfinit(x^2-6);
(09:20) gp > bnfnarrow(K)
%8 = [2, [2], [[5, 1; 0, 1]]]
(09:20) gp > idealred(K, %[3][1])
%9 =
[1 0]

[0 1]


How can I handle a proper narrow reduction  ?

 Thanks,

 Pierre Charollois
 Montreal