#14163: add counit method to QSym
-------------------------------------------------+--------------------------
       Reporter:  saliola                        |         Owner:  
sage-combinat                
           Type:  enhancement                    |        Status:  needs_review 
                
       Priority:  major                          |     Milestone:  sage-5.8     
                
      Component:  combinatorics                  |    Resolution:               
                
       Keywords:  qsym, hopf algebras            |   Work issues:  implement 
the counit         
Report Upstream:  N/A                            |     Reviewers:  Franco 
Saliola, Mike Zabrocki
        Authors:  Mike Zabrocki, Franco Saliola  |     Merged in:               
                
   Dependencies:                                 |      Stopgaps:               
                
-------------------------------------------------+--------------------------
Changes (by {'newvalue': u'Mike Zabrocki, Franco Saliola', 'oldvalue': u'Mike 
Zabrocki'}):

  * reviewer:  => Franco Saliola, Mike Zabrocki
  * author:  Mike Zabrocki => Mike Zabrocki, Franco Saliola


Old description:

> The Hopf algebra of quasisymmetric functions is missing the counit
> method.
> {{{
> sage: QSym = QuasiSymmetricFunctions(QQ)
> sage: F = QSym.Fundamental()
> sage: F.counit
> sage:
> }}}
> Without the counit, {{{_test_antipode}}} at #14161 fails for QSym

New description:

 The Hopf algebra of quasisymmetric functions is missing the counit method.
 {{{
 sage: QSym = QuasiSymmetricFunctions(QQ)
 sage: F = QSym.Fundamental()
 sage: F.counit
 sage:
 }}}
 Without the counit, {{{_test_antipode}}} at #14161 fails for QSym

 Apply: trac_14163_add_counit_qsym-fs.patch

--

Comment:

 Since the code is identical to that of NSym, I put the method in
 {{{ParentMethods}}} for bases of both algebras. Attached it an updated
 patch. Mike, if you like the change, then set this to positive review.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14163#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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