For the record, we had proposed in #18675 to refer to the "graded Hopf algebra" that the topologists use as GradedTopologicalHopfAlgebras and to refer to "Hopf algebras with a grading" that combinatorialists use as GradedCombinatorialHopfAlgebras. It comes up in a name choice in an example in that ticket.
I mainly wanted to know if the current GradedHopfAlgebra structure could handle the two types. If it were just a matter of tests, then *I think* the answer is yes, however then Jean-Baptiste pointed out to me the following example: sage: R = NonCommutativeSymmetricFunctions(QQ).R() sage: (tensor([R[1],R[[]]])+tensor([R[[]],R[1]]))^2 R[] # R[1, 1] + R[] # R[2] + 2*R[1] # R[1] + R[1, 1] # R[] + R[2] # R[] This product is built into the tensor code. It implies that (A # B) * (C # D) = (\mu \otimes \mu) \circ (id \otimes \tau \otimes \tau) (A # B # C # D) where \tau( B # C ) = C # B. I think this is not what we expect for a GradedTopologicalHopfAlgebras, but I guess that the product on the tensor space could be overwritten for those examples. -Mike -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/d/optout.
