[drdeca]

Hm, what about intervals of rationals, and then approximating the intervals with a slightly wider interval in order to make the denominators smaller? I guess the intervals for the real and imaginary components might grow too quickly?

if 0 < a_L < a < a_R , 0 < b_L < b < b_R , then (a + b i)^2 = (a^2 - b^2) + 2 a b i , and a_L^2 - b_R^2 < a^2 - b^2 < a_R^2 - b_L^2 and 2 a_L b_L < 2 a b < 2 a_R b_R ,

uh,

(a_R^2 - b_L^2) - (a_L^2 - b_R^2) = (a_R^2 - a_L^2) + (b_R^2 - b_L^2) = 2 (a_R - a_L) ((a_L + a_R)/2) + 2 (b_R - b_L) ((b_L + b_R)/2)

And, a_R b_R - a_L b_L = a_R b_R - a_R b_L + a_R b_L - a_L b_L = a_R (b_R - b_L) + (a_R - a_L) b_L

So, looks like the size of the intervals are like, (size of the actual coordinate) * (size of interval in previous step), times like, 2?