#8150: various fixes in sage/groups/ and sage/interfaces needed for GAP 4.4.12
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   Reporter:  dimpase         |       Owner:  joyner    
       Type:  defect          |      Status:  new       
   Priority:  major           |   Milestone:  sage-4.3.2
  Component:  group_theory    |    Keywords:            
     Author:  Dima Pasechnik  |    Upstream:  N/A       
   Reviewer:                  |      Merged:            
Work_issues:                  |  
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Comment(by robertwb):

 {{{# random order}}} is preferable to {{{#not tested}}}. I think a lot of
 these could be tested in sensible ways. For example, if word_problem
 returned a list of *tuples* rather than lists (which is more natural),
 then one could do

 {{{
 sage: w = word_problem([a*b,a*c], b*c)
 sage: set(w) == set([(a*b, 1), (a*c, 1)])
 }}}

 Even better,

 {{{
 sage: w = word_problem([a*b,a*c], b*c); w # random solution
 [[a*b, 1], [a*c, 1]]
 sage: w == prod(g^e for g,e in w)
 True
 }}}

 which demonstrates that w is indeed a solution.

 Also, it's clearer to us any and all instead of reduce, if you need to.
 Having huge blocks of {{{#not tested}}} should be avoided unless there's
 no clean way around it.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8150#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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