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...
