Timeline for Nonnegative polynomial in two variables
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 10, 2010 at 10:48 | comment | added | Ilya Nikokoshev | @Qiaochu Yuan, you're right, sorry. | |
| Jan 10, 2010 at 10:45 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
correction
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| Jan 10, 2010 at 1:21 | comment | added | Qiaochu Yuan | I'm not sure I understand. The leading homogeneous term of (x^2 - x)(y + x^{20})^2 is x^{42}, which is a sum of squares. | |
| Jan 9, 2010 at 23:57 | vote | accept | Ilya Nikokoshev | ||
| Jan 9, 2010 at 23:57 | comment | added | Ilya Nikokoshev | @Qiaochu Yuan: no, that's not true. You can always change $(x, y) \to (x, y + x^20)$, so you either prove there are no solutions, or lots of them. This is the primary difficulty I'm having about the problem :) | |
| Jan 9, 2010 at 23:55 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
correction
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| Jan 9, 2010 at 21:52 | comment | added | Qiaochu Yuan | As far as an application to the original problem, I am reasonably sure that the "leading homogeneous term" of the polynomial must be a sum of squares (of polynomials, since it's homogeneous), but I haven't checked that yet either. | |
| Jan 9, 2010 at 21:47 | comment | added | Pete L. Clark | @Ilya: Your "note" is somewhat confusing (I claim that every non-negative function is bounded below!). I think you are missing something like "on $\mathbb{Q} \times \mathbb{Q}$". | |
| Jan 9, 2010 at 21:45 | comment | added | Charles Siegel | So, you've got some answers involving Hilbert 17, but is that really what you're looking for? If not, perhaps you could say something about what kinds of things you're looking for in answers. | |
| Jan 9, 2010 at 21:45 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
fixed grammar
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| Jan 9, 2010 at 21:40 | answer | added | Pete L. Clark | timeline score: 5 | |
| Jan 9, 2010 at 21:10 | answer | added | Charles Siegel | timeline score: 3 | |
| Jan 9, 2010 at 20:44 | history | asked | Ilya Nikokoshev | CC BY-SA 2.5 |