Factoring a polynomial over algebraic numbers?
Actually, what I want is to be able to factor a polynomial over the quadratic closure of the rationals, so that I could factor
x^2-3 say, as
(x+sqrt(3)*(x-sqrt(3)). I don't know enough about factoring algorithms to know whether this is easy or not, but is this at all possible in Sage?
I know I can build an extension field of the rationals by the use of an irreducible quadratic, but that just gives me access to one square root. So if I added
sqrt(3) then I could factorize the example above, but not
x^2-5. Is it possible to include all square roots - in other words, can Sage work with the the field of constructible numbers?