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 the same 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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