Timeline for Polynomials giving Lower Degree Elements in an Algebraic Number Field
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2013 at 2:49 | comment | added | P Vanchinathan | I meant, by higher degree expression, a polynomial of degree more than degree $\deg \alpha/2$, violating my expectation in the original question. | |
| Jun 21, 2013 at 0:59 | comment | added | Gerry Myerson | If $\alpha$ is a root of unity, then $\alpha+\overline\alpha$ always has an expression as a polynomial in $\alpha$, since it's in the field you get by adjoining $\alpha$ to the reals. So I'm not sure I understand your comment. | |
| Jun 21, 2013 at 0:48 | vote | accept | P Vanchinathan | ||
| Jun 21, 2013 at 0:48 | comment | added | P Vanchinathan | Thanks. You have given a method to find examples. For a general root of unity $\alpha$ often it happens that the quadratic number $\alpha+\bar \alpha$ has a higher degree expression as a polynomial in \alpha$. I am trying to prove this having a sizeable number of examples. | |
| Jun 20, 2013 at 2:34 | history | edited | Gerry Myerson | CC BY-SA 3.0 |
added 272 characters in body
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| Jun 20, 2013 at 2:06 | history | answered | Gerry Myerson | CC BY-SA 3.0 |