I think that the general way to go would be to compute a groebner
basis of the ideal we are quotienting by, and then always reduce by
this GB. If i am not mistaken, that is the way that quotients of
multivariate polynomial rings are implemented.

There could be some rings over which we have no groebner basis
algorithm... but i think in those cases there is simply no way to work
with the quotient properly.

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