#14161: add a _test_antipode method for Hopf algebras
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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: Franco Saliola | Merged in:
Dependencies: #14162, #14163 | Stopgaps:
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Comment (by zabrocki):
if you multiply two k-Schurs together the result may or may not be in the
k-Schur space. If not, then just {{{.lift()}}} the result in the
{{{SymmetricFunctions}}}. The coproduct is implemented and is k-Schur
positive.
The coproduct of dual k-Schurs is not implemented. It is a Hopf algebra
if you use the usual coproduct, but it is not clear if this is the
'correct' thing to do. If t=1 then it is probably 'correct' to use the
usual coproduct.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14161#comment:13>
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