ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 21 Jan 2016 04:12:09 -0600Factoring a polynomial over algebraic numbers?https://ask.sagemath.org/question/32308/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](https://en.wikipedia.org/wiki/Constructible_number)?AlasdairThu, 21 Jan 2016 04:12:09 -0600https://ask.sagemath.org/question/32308/