We also should determine how we want to distinguish between (and input) 
A_{+oo} and A_{oo}, i.e., index sets of NN and ZZ. In fact, the only place 
where I really see this fundamentally breaking is the CartanMatrix and 
Dynkin Diagram. All of the root/weight lattice stuff should work since 
those are based around Family and CombinatorialFreeModule (although roots() 
and friends probably won't work so well).

I don't really see a problem with just implementing a subclass of 
CartanType_abstract for A_{+oo}/A_{oo} and allowing the methods to just 
raise NotImplementedError's.

Best,
Travis

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