#9334: Implement Hilbert symbols over number fields
----------------------------------------------------------+-----------------
Reporter: aly.deines | Owner:
davidloeffler
Type: enhancement | Status:
needs_work
Priority: major | Milestone:
sage-5.0
Component: number fields | Keywords:
hilbert symbol
Author: aly.deines | Upstream: N/A
Reviewer: David Loeffler, John Cremona, Marco Streng | Merged:
Work_issues: ReST formatting issues, and more |
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Comment(by mstreng):
And here's another one. In Magma, I get:
{{{
> L := QuadraticField(5);
> O := MaximalOrder(L);
> HilbertSymbol(L!-3, L!-2, 2*O);
1 1/2 + 1/2*i j
}}}
In pari, I get:
{{{
? k = nfinit(x^2-5)
...
? nfhilbert(k, -3, -2, idealprimedec(k, 2)[1])
%2 = 1
}}}
But the patch gives:
{{{
sage: L.<a> = QuadraticField(5)
sage: generalized_hilbert_symbol(L(-3), L(-2), 2*O)
-1
}}}
Something is wrong...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:23>
Sage <http://www.sagemath.org>
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