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?



Unique representation of constructible numbers
A representation of construcible numbers together with algorithms suitable for mechanized computations is given in chapter 4 of [these lecture notes on computer science](http://books.google.com/books?id=nX9En3pwqWsC&pg=PA279&lpg=PA279&dq=representation+of+constructible+numbers&source=bl&ots=2BWAueNw41&sig=mGPSlh0ltREnq6DitnbAhxSSxoY&hl=en&ei=yRs7S53mEommnQObz4TuCA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CAoQ6AEwAQ#v=onepage&q=representation%2520of%2520constructible%2520numbers&f=false) 


