How can I test that an expression is a member of a field extension of $Q$

Asked Dec 31 '17 at 13:53

Active Dec 31 '17 at 15:49

Viewed 79 times

Are there functions in Mathematica that I can use to define a field extension of $Q$? I want to be able to check if an element $a \in Q(\sqrt2)$.

So far I've tried to bypass this with with expressions like

MinimalPolynomial[a, x, Extension -> Sqrt[2]]

and then verifying the degree of the minimal polynomial, but it looks like this doesn't work very well (it insisted on saying that the minimal polynomial of $\sqrt2$ over $Q(\sqrt2)$ was $x^2-2$)

Any ideas?

edited Dec 31 '17 at 15:49

m_goldberg

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asked Dec 31 '17 at 13:53

Andrea Licata

2

ToNumberField[Sqrt[3] + 1, Sqrt[2]]? – Michael E2 Dec 31 '17 at 15:24
What i need is a little bit different. Basically i am programming and i need something that returns "True" or "False" to insert this in a conditional. Something like this:
If["what_im_lookingfor, do this, do other thing] So i don't need a generic message and an useless output – Andrea Licata Dec 31 '17 at 16:41
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FreeQ[Quiet@ ToNumberField[Sqrt[3] + 1, Sqrt[2]], ToNumberField]? – Michael E2 Dec 31 '17 at 16:49
That's it thank you – Andrea Licata Jan 01 '18 at 12:08

How can I test that an expression is a member of a field extension of $Q$

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