#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            |  
----------------------------------------------------------+-----------------
Changes (by mstreng):

  * reviewer:  David Loeffler, John Cremona => David Loeffler, John
               Cremona, Marco Streng


Comment:

 here's a non-documentation reason for `needs_work`:
 {{{
 sage: K.<i> = QuadraticField(-1)
 sage: O = K.maximal_order()
 sage: generalized_hilbert_symbol(K(-1/3), K(-2/3), (1+i)*O)
 ...
 ValueError: self is not a square root mod P^n
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:22>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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