add counit method to QSym

[saliola]

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

CC: @zabrocki

Component: combinatorics

Keywords: qsym, hopf algebras

Author: Mike Zabrocki, Franco Saliola

Reviewer: Franco Saliola, Mike Zabrocki

Merged: sage-5.8.beta1

Issue created by migration from https://trac.sagemath.org/ticket/14163

[zabrocki]

Author: Mike Zabrocki

[zabrocki]

comment:1

Added counit_on_basis to the ParentMethods of the Bases class in QSym. This is a copy of what is in NSym.

[saliola]

apply only this patch

[saliola]

comment:2

Attachment: trac_14163_add_counit_qsym-fs.patch.gz

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.

[saliola]

Reviewer: Franco Saliola, Mike Zabrocki

[saliola]

Changed author from Mike Zabrocki to Mike Zabrocki, Franco Saliola

[nthiery]

comment:3

This really should be added to GradedConnectedHopfAlgebrasWithBasis. But we don't have this category yet (it will be easy when the functorial construction patch will be there). So good for now, but please open a ticket to remind us to create this category and put the counit there!

Thanks!

[jdemeyer]

Changed work issues from implement the counit to none

[jdemeyer]

Merged: sage-5.8.beta1