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quotient ring

I need to compute some things in matrices over a quotient ring. My definition of the quotient ring in question is

v = 8

In particular, I need to quotient out by large (>8 shown above) powers of the ideal I. However, I've noticed that in constructing S, Sage much generate all of the monomials in the power of I which, when v=10, takes quite awhile. Is there any faster/more efficient way to have Sage internally generate S. It actually takes longer to construct S than it does to perform my computations.

This might just be how it is given I'm working over a polynomial ring with four indeterminates...