Hey John,
   IndexedFreeAbelianGroup is also introduced in the ticket. Mainly I want 
to use this to create polynomial rings with arbitrarily indexed variables 
(well any ring with a monomial basis whose variables can be ordered, my 
particular usage will be universal enveloping algebras of a Lie algebra, 
but exterior algebras with infinite generators would be another potential 
usage).
   As for the product_on_basis(), it's more about which type of group 
should we use, additive or multiplicative. I think of the elements of the 
group as actual terms, as opposed to exponent indices. Perhaps this is a 
bikeshed issue since it's an implementation detail and I'm not actually 
implementing any of these rings here.

Hey Simon,
   I believe John was referring to the catalog of groups (which I forgot 
about, thanks!) and proposing a similar catalog for algebras (which I 
support).

Best,
Travis

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