#13687: Parents for groups
----------------------------+-----------------------------------------------
   Reporter:  vbraun        |             Owner:  joyner  
       Type:  enhancement   |            Status:  new     
   Priority:  major         |         Milestone:  sage-5.5
  Component:  group theory  |          Keywords:          
Work issues:                |   Report Upstream:  N/A     
  Reviewers:                |           Authors:          
  Merged in:                |      Dependencies:          
   Stopgaps:                |  
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 Groups are based on the deprecated `ParentWithGens`. This ticket is about
 forward-porting them to the new coercion framework.

 To limit the size of the patchbomb I'm only porting the Abelian groups.
 The rest depends on `old.Group`

 Various oddities needed to be cleaned up in the process:
 * make parents unique and elements immutable (often requires tuples
 instead of lists)
 * rename `AbelianGroup_class.invariants()` ->
 `AbelianGroup_class.gens_orders()` since they are not necessarily the
 abelian invariants (=elementary divisors).
 * rename `element.list()` -> `element.exponents()` for the exponent
 vector.
 * implement a `AbelianGroupWithValues` where you attach values to the
 (abstract) generators. Used in the unit group of a number field, for
 example.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13687>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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