Implements coproduct, antipode and counit in k_dual.py

[zabrocki]

The coalgebra and Hopf structure of the k-bounded quotient were not previously implemented. Ticket #14161 adds a test for the antipode in Hopf algebras which will require these methods.

Apply

• trac_14237_hopf_kdual-mz.patch
• trac_14237-hopf_kdual-review-ts.patch
• trac_14237_change_two_words-mz.patch

Depends on #14228

CC: @anneschilling @saliola @sagetrac-chrisjamesberg

Component: combinatorics

Keywords: coproduct, symmetric functions, antipode

Author: Mike Zabrocki

Reviewer: Travis Scrimshaw

Merged: sage-5.10.beta5

Issue created by migration from https://trac.sagemath.org/ticket/14237

[zabrocki]

comment:1

This ticket may have an impact on #13991. It will certainly add more tests to k_dual.py, but I hope changes to this file will improve performance rather than degrade it.

[zabrocki]

Dependencies: #14228

[zabrocki]

comment:2

I just noticed that #13991 closed and this was a duplicate with #14228. The changes that I make here will have to be made compatible.

[zabrocki]

Attachment: trac_14237_hopf_kdual-mz.patch.gz

[zabrocki]

comment:3

This version applies on #14228 and cleans up the k_dual.py file a bit.

[tscrim]

Attachment: trac_14237-hopf_kdual-review-ts.patch.gz

[tscrim]

comment:4

Hey Mike,

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

Best,

Travis

[tscrim]

Reviewer: Travis Scrimshaw

[zabrocki]

comment:5

Attachment: trac_14237_change_two_words-mz.patch.gz

I completely forgot these tickets were here. I changed a couple of words because I thought the comment in the documentation that I wrote was unclear.

[jdemeyer]

Merged: sage-5.10.beta5