#14367: RuntimeError: There is a bug in the coercion code in Sage (number field 
to
padic)
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       Reporter:  lftabera                        |         Owner:  robertwb 
           Type:  defect                          |        Status:  new      
       Priority:  major                           |     Milestone:  sage-5.10
      Component:  coercion                        |    Resolution:           
       Keywords:  coercion, number field, p-adic  |   Work issues:           
Report Upstream:  N/A                             |     Reviewers:           
        Authors:                                  |     Merged in:           
   Dependencies:                                  |      Stopgaps:           
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Comment (by lftabera):

 I agree with the idea of no guessing. There is no coercion possible form N
 to Zp(7) so here we should raise an error. Note that the problem is not
 that r1 is not invertible in its parent, because it is. The problem is
 that the parent of r1 does not contain any subfield. I am not sure how to
 deal with this. Mathematically, for a simple extension, the parent R of r1
 should be such that:

 - There is a coercion from QQ to R.
 - r1 is an (approximate) root of the defining polynomial of N in R.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14367#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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