Timeline for Roots of anti-palindromic polynomial if coefficients are odd.
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2018 at 23:00 | vote | accept | Student | ||
| Nov 7, 2018 at 22:59 | answer | added | charmd | timeline score: 2 | |
| Nov 4, 2018 at 3:22 | comment | added | Gerry Myerson | I believe, SuperMario, that Fedor's comment was meant to draw your attention to that particular polynomial as an example that might help you to answer your question. You might learn from it something about your kind of polynomial, and its roots, or lack thereof, on the unit circle. | |
| Nov 3, 2018 at 13:05 | comment | added | François Brunault | @SuperMario Your question is vague: do you want to know whether these polynomials may have some roots on the unit circle? Or always have some roots on the unit circle? May have all roots? And so on... You should clarify your post, and include what you know/have tried/expect. | |
| Nov 3, 2018 at 10:05 | comment | added | Student | I was just wondering what the comment meant? | |
| Nov 3, 2018 at 1:41 | comment | added | Gerry Myerson | I'm sure, SuperMario, that you can figure out whether Fedor's polynomial has any roots on the unit circle. | |
| Nov 2, 2018 at 23:48 | comment | added | Student | @FedorPetrov does the polynomial have roots on the unit circle? | |
| Nov 2, 2018 at 23:31 | comment | added | LSpice | As @PhilippLampe pointed out in your other post, your definition of "anti-palindromic polynomial" is not the usual one. Given this, if your definition is really the one you mean to use, it would be a good idea to include it in your posts so people don't keep having to ask. | |
| Nov 2, 2018 at 23:29 | comment | added | Fedor Petrov | hm, what about $1-x+101x^2+x^3+x^4$? | |
| Nov 2, 2018 at 23:18 | comment | added | Student | $P(-x) = x^nP(1/x)$ | |
| Nov 2, 2018 at 22:53 | comment | added | Fedor Petrov | what do you mean by anti palindromic? $a_0+a_1x+\dots+a_nx^n$ where $a_k=-a_{n-k}$ for all $k=0,1,\dots,n$? | |
| Nov 2, 2018 at 22:28 | comment | added | Student | Since $P(1)\equiv P(-1)\equiv 1\pmod{2}$, $\pm 1$ are not roots of $P.$ | |
| Nov 2, 2018 at 21:42 | history | asked | Student | CC BY-SA 4.0 |