It would be nice if the rings made by toField belonged to a new class "Field", so they don't look like polynomial rings.

In line with that, it would be nice if newRing would return a ring that had the
old ring as a base ring (somehow) so that promotion, etc, would work.

Indeed, extending promotion to the entire tree of rings made from others, even
if not supported by fast routines in the engine, would be good for usability.


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Kahle, in particular, would like results of toField to still have a list of generators obtainable with "gens".

See also test/fieldgens.m2
