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Non-linear regression with arbitrary precision arithmetic

I'm looking to do something like this:

R = RealField(1000)
data = [[R(1),R(5)],[R(5),sqrt(R(6))],[R(8),R(9)]]
var('a, b, c, x')
model(x) = a*x*x + b*x + c
find_fit(data, model)

However when I run this a,b and c seem to have been truncated to a double. How would I get arbitrary precision out of find_fit?