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?
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What factors do you expect? – quasi May 12 '17 at 01:12
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The factors should be $(x - \sqrt{-7})(x + \sqrt{-7})$ I don't want to have to introduce the whole set of complex numbers. – Diehardwalnut May 12 '17 at 01:32
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1Fine. In Maple, just multiply those factors, then expand the result. – quasi May 12 '17 at 01:33
1 Answers
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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/
acer
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