I'm trying to develop a java class for exact algebraic numbers. I've come to a little bit of a roadblock as far as this goes. My question right now is how to rationalize these equations, but no-one I've asked seems to know.
Rationalize $$\frac{1}{a+\sqrt[c_1]{b_1}+\sqrt[c_2]{b_2}+\cdots+\sqrt[c_n]{b_n}}$$