#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      |      Merged:                
Work_issues:  ReST formatting issues, and more  |  
------------------------------------------------+---------------------------
Changes (by rlm):

  * status:  needs_review => needs_work


Comment:

 Based on 4.5.3.alpha1:

 {{{
 sage -t  sage/rings/number_field/number_field_ideal.py
 **********************************************************************
 File "/home/rlmill/sage-4.5.3.alpha1/devel/sage-
 main/sage/rings/number_field/number_field_ideal.py", line 1212:
     sage: P.uniformizer()
 Expected:
     a + 4
 Got:
     -2*a + 1
 **********************************************************************
 File "/home/rlmill/sage-4.5.3.alpha1/devel/sage-
 main/sage/rings/number_field/number_field_ideal.py", line 1219:
     sage: P.uniformizer()
 Expected:
     -7*a^4 + 13*a^3 - 13*a^2 - 2*a + 50
 Got:
     a^4 - a^3 + a^2 - a + 1
 **********************************************************************
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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