Implements antipode and counit in new_kschur.py

[zabrocki]

At t=1 the space where the k-Schur functions live is a Hopf algebra but the antipode and counit were never implemented because they were not required. Ticket #14161 adds a test for the antipode that requires a counit method and so doc tests in new_kschur.py will fail unless these methods are implemented.

Apply

• trac_14235_hopf_kschur-mz.patch
• trac_14235-hopf_kschur-review-ts.patch

Depends on #13743

CC: @anneschilling @saliola @sagetrac-chrisjamesberg

Component: combinatorics

Keywords: symmetric functions, antipode

Author: Mike Zabrocki

Reviewer: Travis Scrimshaw

Merged: sage-5.10.beta5

Issue created by migration from https://trac.sagemath.org/ticket/14235

[zabrocki]

comment:1

Not sure whether to call this a 'defect' or an 'enhancement'. I am going with the latter.

I also am moving the coproduct method from the ElementMethods to the ParentMethods.

[zabrocki]

comment:3

This patch is now rebased against #13743

[zabrocki]

Dependencies: #13743

[fchapoton]

comment:4

There is a typo here :

counit is the constant terms

should be

counit is the constant term

[zabrocki]

comment:5

Attachment: trac_14235_hopf_kschur-mz.patch.gz

I've corrected this typo.

[tscrim]

comment:6

Attachment: trac_14235-hopf_kschur-review-ts.patch.gz

Hey Mike,

I've uploaded a review patch which makes some minor tweaks to the doc. If you're happy with the changes, you can set this to positive review.

Best,

Travis

[tscrim]

Reviewer: Travis Scrimshaw

[zabrocki]

comment:8

Thanks Travis for coming back to both of these patches. They long fell off of my radar.
-Mike

[jdemeyer]

Merged: sage-5.10.beta5