Given in this problem is a set of values $0 \le c_{a,b} < n$, where $0 \le a < n$ and $0 \le b < n$.The problem is to find the following sum as quickly as possible:$$\sum_{a,b}{c_{a,b}x^a y^b} \bmod n$$Here $x$ and $y$ are also assumed to be integers modulo $n$.I'd like to know what the best method/approach is to solving this problem, and what kinds of worst-case behavior we can expect to get the sum.Are there any similar problems whose solutions may help with this?SOME NAIVE IDEASThere are $n^2$ different constants and only $n$ different possible assignments for each $c_{a,b}$, so it seems that grouping some of the coefficients together is the best way to go.  However, beyond simple ideas, I'm not sure what will work best.  I'm hoping I can get some good suggestions.MOTIVATIONMy motivation for tackling this particular problem is that its solution may help improve the bounds of #3-SAT by some small degree.  However, the relation between the two is fairly complicated.
How well can we do with this variable assignment problem?
ds.algorithms;worst case