#12116: perfect_power for integers
--------------------------------+-------------------------------------------
   Reporter:  roed              |          Owner:  AlexGhitza                   
          
       Type:  enhancement       |         Status:  needs_work                   
          
   Priority:  major             |      Milestone:  sage-5.0                     
          
  Component:  basic arithmetic  |       Keywords:                               
          
Work_issues:                    |       Upstream:  Completely fixed; Fix 
reported upstream
   Reviewer:  David Loeffler    |         Author:  David Roe                    
          
     Merged:                    |   Dependencies:  #10596, #12363               
          
--------------------------------+-------------------------------------------
Changes (by jdemeyer):

  * status:  positive_review => needs_work
  * dependencies:  #10596 => #10596, #12363
  * upstream:  Fixed upstream, but not in a stable release. => Completely
               fixed; Fix reported upstream


Old description:

> Currently there are two functions for testing whether an integer is a
> perfect power:
> {{{
> sage: 8.is_power()
> True
> sage: 8.is_perfect_power()
> True
> }}}
>
>  * This patch deprecates `is_perfect_power`.
>  * It implements a new function, `perfect_power`, wrapping Pari's
> `ispower` function, expressing an integer in the form a^b^ with `b`
> maximal.  This revealed a bug in Pari for negative even powers: I'm in
> the process of reporting it.
>  * It adds cross references between `is_power`, `is_power_of`,
> `is_prime_power` and `perfect_power`.

New description:

 Currently there are two functions for testing whether an integer is a
 perfect power:
 {{{
 sage: 8.is_power()
 True
 sage: 8.is_perfect_power()
 True
 }}}

  * This patch deprecates `is_power`.
  * It implements a new function, `perfect_power`, wrapping PARI's
 `ispower` function, expressing an integer in the form a^b^ with `b`
 maximal.  This revealed a bug in PARI for negative even powers, reported
 and fixed at [http://pari.math.u-bordeaux.fr/cgi-
 bin/bugreport.cgi?bug=1259&archive=yes]
  * It adds cross references between `is_perfect_power`, `is_power_of`,
 `is_prime_power` and `perfect_power`.

--

Comment:

 The upstream fix is in Sage now (#12363).  Could you remove the workaround
 code from the patch?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12116#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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