# Unique representation of constructible numbers

I am interested in programmatically working with constructible numbers (the closure of the rational numbers under square roots). In order to perform comparisons between numbers I believe I would need a unique (symbolic) representation for them. Does such a thing exist, or what are relevant references for this kind of thing?

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When you say "comparison" do you mean "test for equality" or are you trying to determine if one is greater than the other? –  Qiaochu Yuan Dec 30 '09 at 8:08