Slightly unrelated, there is the following note at the top of
sage/algebras/group_algebra.py:
"""
-- It seems to be impossible to make this fit nicely with Sage's coercion
model. The problem is that (for example) if G is the additive group (ZZ,+),
and R = ZZ[G] is its group ring, then the integer 2 can be coerced into R
in two ways -- via G, or via the base ring -- and *the answers are
different*. In practice we get around this by preventing elements of G
coercing automatically into ZZ[G], which is a shame, but makes more sense
than preventing elements of the base ring doing so.
"""
I don't really understand the issue.
Does anybody know an explicit example where this would indeed be a problem?
I believe the whole point of a group algebra is to linearize G, i.e.
embed it into an R-module R[G]. With that in mind, the map from R to
R[G] seems less important, not more -- it is the R-action what matters
on that front. I think I'd rather sacrifice the automatic coercion
from R instead of the one from G if one of the two really has to go.
What do you think?
Gonzalo
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