#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, Marco Streng | Upstream: N/A
Reviewer: David Loeffler, John Cremona, Marco Streng | Merged:
Work_issues: bug in Pari 2.4.3 |
----------------------------------------------------------+-----------------
Changes (by newvalueoldvalue):
* work_issues: ReST formatting issues, and more => bug in Pari 2.4.3
* author: aly.deines => Aly Deines, Marco Streng
Old description:
> Hilbert symbol over number fields may be implemented using an algorithm
> described in John Voigt's paper "Identifying the Matrix Ring: Algorithms
> for Quaternion Algebras and Quadratic Forms".
New description:
Pari has Hilbert symbols for number fields. Hilbert symbols can be
implemented by wrapping pari's function `nfhilbert`.
--
Comment:
All that needed to be done was wrap pari's nfhilbert function and copy
Aly's doctests, but...
One of those doctests revealed yet another bug introduced by the pari
upgrade. See [http://pari.math.u-bordeaux.fr/cgi-
bin/bugreport.cgi?bug=1147]
Apply trac_9334_nfhilbert.patch once pari bug 1147 is fixed and that fix
reaches Sage.
Possible future improvements:
* implement also for relative number fields by simply delegating to the
absolute case
* implement also for QQ by wrapping the global function hilbert_symbol as
a member of QQ
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:25>
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