#14161: add a _test_antipode method for Hopf algebras
----------------------------------+-----------------------------------------
       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:                  |     Merged in:               
   Dependencies:  #14162, #14163  |      Stopgaps:               
----------------------------------+-----------------------------------------

Old description:

> Desired doctests:
> {{{
>                 sage: R = NonCommutativeSymmetricFunctions(QQ).ribbon()
>                 sage: R._test_antipode()
>
>             ::
>
>                 sage: s = SymmetricFunctions(QQ).schur()
>                 sage: s._test_antipode()
> }}}
>
> This would have caught the bug in #14160.

New description:

 Desired doctests:
 {{{
                 sage: R = NonCommutativeSymmetricFunctions(QQ).ribbon()
                 sage: R._test_antipode()

             ::

                 sage: s = SymmetricFunctions(QQ).schur()
                 sage: s._test_antipode()
 }}}
 This would have caught the bug in #14160.

 Apply : trac_14161-fs.2.patch

--

Comment (by saliola):

 Thanks for catching that, John. I deleted the corresponding lines.

 (For the record, Mike and I discussed using {{{is_commutative}}} and
 {{{is_cocommutative}}}, but neither seems to be reliably implemented. So
 we won't test it until the appropriate categories are implemented.)

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14161#comment:8>
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