Hi,
This question is kind of directed at Nicolas, but I'll accept the answer
from anyone who knows the answer.
On ticket #18675 there was a discussion about the definition of
GradedHopfAlgebra. It turns out that topologists use a Koszul sign
convention in one of the bi-algebra axioms.
$$(\mu \otimes \mu) \circ (id \otimes \tau \otimes id) \circ (\Delta
\otimes \Delta) = \Delta \circ \mu$$
In combinatorics the twist map is $\tau(x \otimes y) = y \otimes x$
For a topologist a "graded Hopf algebra" implies that the twist map should
satisfy $\tau(x \otimes y) = (-1)^{deg(x)deg(y)} y \otimes x$
I imagine that a Hopf algebra satisfying the first twist satisfies the
tests imposed in the category of GradedHopfAlgebra. Does the second?
If the second does not satisfy the conditions of being a GradedHopfAlgebra,
where is the code in Sage that would cause that Hopf algebra to fail tests?
-Mike
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