> The question is really: is the map between representations of the same
> finite field, which differ only in variable name, "canonical"?

I would say that there is no big risk to do that, though I am not at
all knowledgeable on those parts of the code. If it can be dangerous
but can be detected, however, it would be cool if an error message
could hint at it, e.g. "the generators have different names".

Though really, "checking" things by comparing the strings used to
describe generators does not look very reliable either. Especially
since because of this behaviour I will now start using the same string
'a' everywhere, just to avoid it.

Nathann

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