#14161: add a _test_antipode method for Hopf algebras
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       Reporter:  saliola         |         Owner:  sage-combinat
           Type:  enhancement     |        Status:  needs_work   
       Priority:  major           |     Milestone:  sage-5.8     
      Component:  combinatorics   |    Resolution:               
       Keywords:  hopf algebras   |   Work issues:               
Report Upstream:  N/A             |     Reviewers:               
        Authors:  Franco Saliola  |     Merged in:               
   Dependencies:  #14162, #14163  |      Stopgaps:               
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Comment (by saliola):

 Replying to [comment:15 chrisjamesberg]:
 > I vote to keep as a Hopf algebra! If you call something a Hopf algebra,
 do you have to implement the antipode? Isn't "Not implemented" acceptable?
 It's still a Hopf algebra even if it doesn't know how to compute the
 antipode.

 I'd like to keep it as a Hopf algebra, too. Especially since we know how
 to compute the antipode (see Mike's comment). Can you implement it?

 > I think the description of this ticket could be a little more
 informative than just a few doctests. Without reading the code, I'm not
 exactly sure what this ticket is about.

 I thought it was pretty self-explanatory based on the understanding that
 the purpose of all the {{{_test_*}}} methods is to make sure that
 something isn't obviously wrong with the code by running a few tests. Such
 a test would/should have caught the bug we found with the antipode of NSym
 because it failed the defining condition for an antipode.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14161#comment:18>
Sage <http://www.sagemath.org>
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