#9334: hilbert symbols!!!
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Reporter: aly.deines | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.0
Component: number fields | Keywords: hilbert symbol
Author: aly.deines | Upstream: N/A
Reviewer: David Loeffler, John Cremona | Merged:
Work_issues: ReST formatting issues, and more |
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Comment(by mstreng):
Great, I could use this.
While you are still at it, I have a small wish list as well. Could you
* Let the generalized even Hilbert symbol accept fractions (as the odd
one and the QQ one do)?
{{{
sage: hilbert_symbol(1/3, 1, 2)
1
sage: K.<i> = QuadraticField(-1)
sage: O = K.maximal_order()
sage: generalized_hilbert_symbol(K(1/2), K(1), 3*O)
1
sage: generalized_hilbert_symbol(K(1/3), K(1), (1+i)*O)
NotImplementedError: inverse_mod is not implemented for non-integral
elements
}}}
* Also add the Hilbert symbol for infinite places? See e.g.
{{{
sage: hilbert_symbol(-1, -1, -1)
-1
}}}
This is almost trivial compared to what you've already done. I have
code, contact me if you have questions.
* Correct the doc text. The doc of generalized_even_hilbert_symbol should
say that P must divide 2, while generalized_hilbert_symbol should not say
that P must be odd
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:9>
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