# quotient ring

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

```
R.<A,B,C,D>=QQ[]
I=R.ideal(A,B,C,D)
v = 8
S.<a,b,c,d>=R.quotient_ring(I^(v+1))
```

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...