Timeline for Smallest root of a degree 3 polynomial
Current License: CC BY-SA 4.0
25 events
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| Sep 19 at 4:01 | history | edited | GH from MO |
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| Sep 17 at 13:48 | history | edited | Venus |
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| Sep 16 at 8:52 | history | edited | GH from MO |
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| Sep 16 at 6:41 | comment | added | GH from MO | I added a proof which requires no machine calculation and is cleaner (in my opinion) than the two proofs already posted. Moreover, it shows that there is a real root not exceeding $(5-\sqrt{15})/10$, and this estimate is optimal. | |
| Sep 16 at 6:06 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 16 at 5:31 | answer | added | GH from MO | timeline score: 12 | |
| Sep 15 at 19:37 | comment | added | Steven Stadnicki | @IosifPinelis I think it's an excellent question and have certainly not downvoted/closevoted, but I suspect the folks who are are hoping for more context; it's clear that this polynomial comes from somewhere rather than appearing like Venus from the waves, and it would be helpful/interesting/etc. to know its origins. | |
| Sep 15 at 16:38 | comment | added | GH from MO | I removed the tag "root-systems" as it is not relevant for the problem. Regarding root systems, see en.wikipedia.org/wiki/Root_system | |
| Sep 15 at 16:36 | history | edited | GH from MO |
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| Sep 15 at 14:57 | history | became hot network question | |||
| Sep 15 at 14:45 | answer | added | River Li | timeline score: 7 | |
| Sep 15 at 13:42 | comment | added | Iosif Pinelis | I don't understand the close votes. The problem does not seem quite trivial, and it could possibly have arisen in some research. | |
| Sep 15 at 13:37 | answer | added | Iosif Pinelis | timeline score: 7 | |
| Sep 15 at 12:10 | history | edited | Venus |
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| Sep 15 at 10:14 | history | edited | Venus | CC BY-SA 4.0 |
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| Sep 15 at 10:03 | comment | added | Venus | @FedorPetrov Do you have any insights on finding the answer? Thanks. | |
| Sep 15 at 9:02 | comment | added | Venus | @FedorPetrov Thank you for your comment. It has been revised. Thanks. | |
| Sep 15 at 9:01 | history | edited | Venus | CC BY-SA 4.0 |
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| Sep 15 at 8:38 | history | edited | Venus | CC BY-SA 4.0 |
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| Sep 15 at 7:06 | comment | added | Fedor Petrov | I am suspicious about conditions on $\alpha, \beta, \gamma$: the restriction $\alpha+\beta+\gamma\le 2\pi$ seems useless, since if it does not hold, you may replace $\alpha, \beta$ to $\pi-\alpha, \pi-\beta$ and the polynomial does not change. Are you sure that we do not require additionally that $\alpha+\beta\ge \gamma$ etc? | |
| Sep 15 at 6:58 | comment | added | Venus | @FedorPetrov It may not be completely that, but do you have any insights on finding the answer regarding the algebraic or analytic property of polynomials? Thanks. | |
| Sep 15 at 6:32 | review | Close votes | |||
| Sep 20 at 8:09 | |||||
| Sep 15 at 5:56 | comment | added | Fedor Petrov | This looks like a characteristic polynomial of a certain $3\times 3$ matrix, is not it arised this way? | |
| Sep 15 at 5:29 | comment | added | Venus | I have performed numerous computations but have not found any counterexample. | |
| Sep 15 at 5:28 | history | asked | Venus | CC BY-SA 4.0 |