Talk:Minimal polynomial of 2cos(2pi/n)

Requested move 25 April 2021

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: no consensus. (closed by non-admin page mover) ~ Aseleste (t, e | c, l) 14:49, 18 May 2021 (UTC)

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Minimal polynomial of 2cos(2pi/n) → Real parts of roots of unity – Implausible search term. See also Wikipedia_talk:WikiProject_Mathematics#Minimal_polynomial_of_2_cos(2π/n). Merger was considered, but we first need a better title at which to store the merged content for attribution. –LaundryPizza03 (dc̄) 13:14, 25 April 2021 (UTC) —Relisting. Bada Kaji (talk) 11:19, 11 May 2021 (UTC)

• Support, as I have suggested the move in the above linked discussion. I agree to not leave a redirect. D.Lazard (talk) 13:45, 25 April 2021 (UTC)
• Oppose – The current title matches the title of one of its sources, so is at least source based. There's no requirement that a title be a plausible search term. If "Real parts of roots of unity" is a plausbile search term, a redirect will handle that; so far, it looks like not. Dicklyon (talk) 05:13, 28 April 2021 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Perhaps the discussion above should be reopened. The current article title is screwy. The given title is fine for an article in American Math Monthly, where the readers will already know what roots of unity are, and will realize the significance of the article. However, on Wikipedia, this title is utterly inappropriate, since this article is about ... well, that's the problem, isn't it? Its not so much about the real part of the roots of unity, as it is about the polynomial that relates them. And I can't think of a particularly appropriate title that says this in some appropriate way. 67.198.37.16 (talk) 20:20, 14 January 2024 (UTC)

Sure that the most accurate title would be Minimal polynomials of real parts of foots of unity. However this title is clearly too long. Also, it implies the knowlege of a theorem, namely that these real parts are algebraic numbers (otherwise, there would not exist minimal polynomials). Once one knows that these numbers are algebraic, their study becomes the same as the study of their minimal polynomial. Thus Real parts of roots of unity seems the best compromise between WP:CRITERIA. D.Lazard (talk) 09:29, 15 January 2024 (UTC)

Hmm. Duckduckgo gets zero meaningful hits for "real part of root of unity" while "Minimal polynomial of 2cos(2pi/n)" gets six strong hits on the first page, including several math-overflow questions, several PDF's, and a jstor to the original article. So now I have cold feet. 67.198.37.16 (talk) 07:17, 4 February 2024 (UTC)

Error in Chebyshev section

The result of Watkins and Zeitlin quoted in this section is for $\Psi _{n}(x)$ being the minimal polynomial of $\cos(2\pi /n)$ and not $2\cos(2\pi /n)$. It was not immediately clear the best way to fix this issue (either rename the polynomials or adjust the result with the appropriate power of 2). —-72.19.117.37 (talk) 17:27, 14 June 2021 (UTC)

It seems that the correct formulas are got by replacing $2^{s}\prod \limits _{d\mid n}\Psi _{d}(x)$ by $\prod \limits _{d\mid n}\Psi _{d}(2x).$ However this must checked with the original paper. By the way, the monic minimal polynomial of $\cos(2\pi /n)$ must be avoided, since its coefficients are not integers. The primitive minimal polynomial of $\cos(2\pi /n)$ is more convenient, and is $\Psi _{d}(2x).$ D.Lazard (talk) 09:14, 15 June 2021 (UTC)