#4376: Implement conversion of power series over more rings (e.g. GF(p)) to pari
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   Reporter:  cremona                         |       Owner:  was               
  
       Type:  enhancement                     |      Status:  needs_work        
  
   Priority:  major                           |   Milestone:  sage-4.6.2        
  
  Component:  interfaces                      |    Keywords:  power series pari 
gp
     Author:  Francis Clarke, Jeroen Demeyer  |    Upstream:  N/A               
  
   Reviewer:  Marco Streng                    |      Merged:                    
  
Work_issues:                                  |  
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Comment(by fwclarke):

 Replying to [comment:9 jdemeyer]:

 > Test failures on sage-4.6.2.alpha1:
 > ...

 What's happened is that #7644 means that many more series can be converted
 to Pari and reversion performed using `sereverse`.  But when the degree-
 one coefficient is not a unit, converting the result back to Sage has
 exposed the following problem:
 {{{
 sage: P.<x> = Q[]
 sage: Q = P.fraction_field()
 sage: Q(1/x)
 1/x
 sage: Q(pari(1/x))
 0
 }}}
 This is caused by
 {{{
 sage: P(pari(1/x))
 0
 }}}
 whereas `P(1/x)` raises `TypeError: denominator must be a unit`.

 The other group of failures is caused when conversion to a Pari series is
 successful but reversion raises a Pari error.

 I will shortly post a patch which sorts these difficulties out. I've added
 a doctest for `reversion` in order to provide another example where Pari
 fails and the Lagrange inversion code needs to be used.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4376#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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