I have a sum of square roots each with a coefficient, for example like this:
√2 + 2√3 - 4√5 + 2√6 + ...
How do I know if the sum is positive or negative without calculating each square root and thus the actual sum?
Background: I am working on a data type for python which uses integers in its inner structure to store square roots. The type uses the idea, that the integers in python can be infinitely big and precise, not like the floats. This data type is very practical to calculate different things, for example the Fibonacci numbers using the golden ration φ. My data type is so far ready, but the only operator is missing is the comparison. Comparing sums of square roots means proving the sign of their difference.
Edit: Apparently this is a still open problem and is yet not solved: Sum of radicals