> sage: G.<a, b, c> = FreeGroup()
> sage: G
> Free Group on the Set {a, c, b}
> sage: b
> c
>
> This is probably due more to crappy programming on my part rather than
> the Set issue, but the latter did confuse me.
I think this is due to a poor definition: the decision was made that
variables are named and order matters. So G.<a,b,c> = FreeGroup() and
G.<a,c,b> = FreeGroup() are different objects -- the lists of
generators have different names, and that makes them distinct. So
printing the "Free Group on the Set {a, b, c}" is misleading because
the current convention is that "FG on a, b" and "FG on b, a" are
distinct.
Nick
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