Polynomial factorization and root finding

The factor command now accepts an additional argument, an algebraic extension specifying an algebraic number field over which the polynomial is to be factored. The extension can be specified as a single RootOf or radical, or in the case of multiple extensions, a list or set of such. Example: factor the polynomial over

    > factor(y^4-2,sqrt(2));

                              2    1/2    2    1/2
                            (y  + 2   ) (y  - 2   )

    > alias(alpha = RootOf(x^2-2));
    > factor(y^4-2,alpha);

                             2            2
                           (y  + alpha) (y  - alpha)

An algebraic extension can also be given to the roots and irreduc functions.