Algebraic extension by $\sqrt{-7}$

Question

In trying to find the Galois group of a polynomial, I am trying to see if adjoining $\sqrt{-7}$ can split the polynomial but entering factor(x^2 + 7 , $\sqrt{-7}$) is invalid. How can I accomplish this?

Answer 1

So your problem is with the particular Maple syntax?

factor(x^2+7, (-7)^(1/2));

           /         (1/2)\ /        (1/2)\
          -\-x + (-7)     / \x + (-7)     /

note:

sqrt(-7);

                     (1/2)
                  I 7     

(-7)^(1/2);

                      (1/2)
                  (-7)

And you were trying not to have to do it like this?

factor(x^2+7, {sqrt(-1),sqrt(7)});

            /   (1/2)    \ /   (1/2)    \
           -\I 7      - x/ \I 7      + x/