How can I express Sqrt[2] as an element in the field Q(2^(1/4))?

Asked Apr 07 '16 at 22:08

Active Apr 08 '16 at 12:46

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If I input: ToNumberField[Sqrt[2], 2^(1/4)]

Mathematica returns: AlgebraicNumber[Root[-2 + #1^4 &, 2], {0, 0, 1, 0}]

How would I know which root of x^4 - 2 Mathematica is referring to here? In this simple example it must mean either of the two real roots of x^ - 2. But how would I know this otherwise. In other words, my question is what does the 2 in the returned expression mean?

edited Apr 08 '16 at 12:46

m0nhawk

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asked Apr 07 '16 at 22:08

Geoffrey Critzer

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It refers to a "canonical" numbering. Without getting into that, I'll point out that you can apply N[] to see a numeric approximation thereof. – Daniel Lichtblau Apr 08 '16 at 01:28
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…or apply ToRadicals[] to it to see the corresponding radical form. – J. M.'s missing motivation Apr 08 '16 at 02:08

How can I express Sqrt[2] as an element in the field Q(2^(1/4))?

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