#12575: Generic p-adic log and exp
-----------------------------------------------------------+----------------
       Reporter:  mmasdeu                                  |         Owner:     
                                    
           Type:  enhancement                              |        Status:  
needs_review                           
       Priority:  major                                    |     Milestone:  
sage-5.7                               
      Component:  padics                                   |    Resolution:     
                                    
       Keywords:  exp, log, padic                          |   Work issues:     
                                    
Report Upstream:  N/A                                      |     Reviewers:  
David Loeffler, David Roe, Julian Rueth
        Authors:  Amnon Besser, Marc Masdeu, Julian Rueth  |     Merged in:     
                                    
   Dependencies:  #13539                                   |      Stopgaps:     
                                    
-----------------------------------------------------------+----------------
Changes (by {'newvalue': u'Amnon Besser, Marc Masdeu, Julian Rueth', 
'oldvalue': u'Amnon Besser, Marc Masdeu'}):

  * owner:  saraedum =>
  * reviewer:  David Loeffler, David Roe => David Loeffler, David Roe,
               Julian Rueth
  * dependencies:  => #13539
  * author:  Amnon Besser, Marc Masdeu => Amnon Besser, Marc Masdeu, Julian
             Rueth


Comment:

 I found several issues. I added a patch which should fix them:

 * log sometimes didn't work in the capped-absolute case (especially over
 extension fields)
 * the bound {{{max_term}}} in {{{_exp}}} was incorrect which made
 {{{exp}}} and {{{log}}} not inverse to each other in some cases
 * the capped-absolute/fixed-mod implementation of {{{exp}}} somehow didn't
 get some of the digits right (I tried to find out why, but couldn't figure
 it out). I rewrote {{{_exp}}} which is now shorter and works in the cases
 that didn't work before. In particular it doesn't lift the input to the
 integers anymore. Is there a reason why we should work over the integers?
 * I believe that the check for convergence of the exponential series was
 incorrect.

 Apart from that, I tried to simplify the code in a few places and turned
 the cached values into actual {{{cached_methods}}} -- if someone dislikes
 that latter change, I don't mind undoing it.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12575#comment:21>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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