Well, I actually had in mind to base my implementation of the Groebner walk off these classes, this is why I was so eager about discussing the topic.
I think this is the part which I really don't understand. Groebner basis code works for very specific rings (namely polynomial rings in finitely many commuting indeterminates, or certain special localisations thereof -- you probably know this better than I do) and does something very special - in your case taking a very specific list of elements of the ring, and turning them into another very specific list of elements. I don't see how an abstract ring framework will be of use here at all -- since the only ring your code works with is PolynomialRing anyway. It is not clear to me either how a class representing ideals is helpful for you -- as I see it, groebner bases are an implementation detail of ideals, so an ideal class creates groebner bases, but not the other way round.
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