#6292: Converting elements in AbelianGroup to gap element
--------------------------+-------------------------------------------------
 Reporter:  jlefebvre     |       Owner:  joyner      
     Type:  defect        |      Status:  new         
 Priority:  major         |   Milestone:  sage-4.0.2  
Component:  group_theory  |    Keywords:  AbelianGroup
 Reviewer:                |      Author:              
   Merged:                |  
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 Some trouble in converting elements in AbelianGroup to gap elements
 For example we can do this;
 {{{
 sage: G = SymmetricGroup(5)
 sage: g = G.list()[2]
 sage: H = gap(G)
 sage: g in H
 True
 }}}
 But not this;
 {{{
 sage: G = AbelianGroup([2,2])
 sage: g = G.list()[2]
 sage: H = gap(G)
 sage: g in H
 [...]
 TypeError: Gap produced error output
 Variable: 'f0' must have a value
 }}}


 Similarly we can't go back the other way around.
 That is we can do this;
 {{{
 sage: G = SymmetricGroup(5)
 sage: H = gap(G)
 sage: r = H.ConjugacyClasses()[2].Representative()
 sage: type(r)
 <class 'sage.interfaces.gap.GapElement'>
 sage: r in G
 True
 sage: G(r)
 (1,2)
 }}}

 But not this
 {{{
 sage: G = AbelianGroup([2,2])
 sage: H = gap(G)
 sage: r = H.ConjugacyClasses()[2].Representative()
 sage: r
 f1
 sage: r in G
 False
 sage: G(r)
 [...]
 TypeError: Argument x (= f1) is of wrong type.
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6292>
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