---------- Forwarded message ----------
From: Djordjo Milovic <[email protected]>
Date: 23 January 2015 at 12:51
Subject: [sage-devel] trivial Artin symbols
To: [email protected]
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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