Timeline for Symmetric version of Hilbert's seventeenth problem?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2023 at 13:14 | comment | added | Fedor Petrov | @SamHopkins is $(x-y)^2$ a sum of squares of symmetric rational functions? I doubt, since any such function must be divisible by $x-y$, thus (being symmetric) by $(x-y)^2$, thus its square is divisible by $(x-y)^4$ | |
| Mar 25, 2023 at 13:21 | comment | added | Sam Hopkins | @FedericoPoloni Right. I guess a specific question you could ask is: is it possible to express a nonnegative, symmetric polynomial as a sum of squares of symmetric rational functions? Maybe this is obvious? But I don't quite see it... | |
| Mar 25, 2023 at 10:33 | comment | added | Federico Poloni | Does the result include anything about non-negativity and squares? Otherwise, how does it apply to the question? | |
| Mar 24, 2023 at 21:05 | history | answered | Bazin | CC BY-SA 4.0 |