#9334: Implement Hilbert symbols over number fields
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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 | Merged:
Work_issues: ReST formatting issues, and more |
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Changes (by mstreng):
* status: needs_review => needs_work
Comment:
Here are some comments have already been mentioned above:
* why aren't generalized_hilbert_symbol and
generalized_even_hilbert_symbol in the same file? (e.g. both in
number_field as John suggested)
* the documentation of generalized_hilbert_symbol says that the prime
should be odd, which isn't necessary, in fact, it would be good to have an
even example in the doctest so this functionality doesn't get broken
* the documentation of generalized_even_hilbert_symbol doesn't say that
the prime must be even, which it should!
Also, generalized_even_hilbert_symbol is less powerful than the general
one:
{{{
sage: K.<i> = QuadraticField(-1)
sage: O = K.maximal_order()
sage: generalized_hilbert_symbol(K(1/3), K(1), (1+i)*O)
1
sage: generalized_even_hilbert_symbol(K(1/3), K(1), (1+i)*O)
...
NotImplementedError: inverse_mod is not implemented for non-integral
elements
}}}
So I guess the documentation of generalized_even_hilbert_symbol should say
that the input should consist of integral elements? Possibly the
documentation of generalized_even_hilbert_symbol could say that this is
simply an auxiliary function and the user should call
generalized_hilbert_symbol instead?
needs_work because of the documentation issues for
generalized_even_hilbert_symbol
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:21>
Sage <http://www.sagemath.org>
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