Hi Djordjo,
It turns out that in your example the decomposition group is represented
internally as a permutation group on the wrong number of elements. I am
now testing a fix; see http://trac.sagemath.org/ticket/17664 .
Peter
> ---------- Forwarded message ----------
> From: Djordjo Milovic <dzm...@gmail.com>
> Date: 23 January 2015 at 12:51
> Subject: [sage-devel] trivial Artin symbols
> To: sage-devel@googlegroups.com
>
>
> Hi all,
>
> Can someone explain why there is an error when I try to compute an
> Artin symbol which is supposed to be trivial? In the following
> example, I am computing Artin symbols of some odd primes in the
> quadratic extension of discriminant -4. The Artin symbols of primes
> $\equiv 3\bmod 4$ are computed correctly, while there is an error for
> every $p\equiv 1\bmod 4$.
>
> I know this is a simple example and I don't need Sage to compute it
> for me, but I am getting a similar error in a more complicated
> situation where I can't do computations by hand.
>
> Thanks!
> Djordjo
>
> Sage code:
>
> QI.<ii> = NumberField(x^2+1)
> L = QI.absolute_field('c')
> G = L.galois_group()
> print G
> print [G.artin_symbol(P) for P in L.primes_above(3)]
> print [G.artin_symbol(P) for P in L.primes_above(7)]
> print [G.artin_symbol(P) for P in L.primes_above(11)]
> print [G.artin_symbol(P) for P in L.primes_above(5)]
>
> Output:
>
> Galois group of Number Field in c with defining polynomial x^2 + 1
> [(1,2)]
> [(1,2)]
> [(1,2)]
> Traceback (click to the left of this block for traceback)
> ...
> sage.libs.pari.gen.PariError: incorrect permutation in permtopol
>
>
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