Timeline for When is a power of a nonnegative polynomial a sum of squares?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Dec 12, 2022 at 16:48 | comment | added | Chris Leary | @Gerry Myerson - It pays to read questions carefully. Upon rereading, I missed that $f$ was generally to be nonnegative. | |
| Dec 12, 2022 at 14:46 | comment | added | Chris Leary | @Gerry Myerson - I was wondering if it came down to strictly a sum, with no subtractions. Thanks for clarifying. | |
| Dec 10, 2022 at 22:08 | comment | added | Gerry Myerson | @Chris, there's a difference between a sum and a difference. | |
| Dec 10, 2022 at 19:24 | comment | added | Chris Leary | @user2529 - I am confused by the terminology "sum of squares." If we think of Motzkin's example as a polynomial with real coefficients, aren't each of the monomial terms squares. Please enlighten me as to where my confusion lies. | |
| Dec 10, 2022 at 17:23 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title, while this is on the front page
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| Dec 10, 2022 at 12:10 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 9, 2011 at 5:30 | history | edited | user2529 | CC BY-SA 2.5 |
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| Feb 2, 2011 at 14:05 | history | edited | user2529 | CC BY-SA 2.5 |
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| Feb 2, 2011 at 14:00 | vote | accept | CommunityBot | ||
| Feb 2, 2011 at 14:00 | history | bounty ended | CommunityBot | ||
| Jan 31, 2011 at 15:04 | answer | added | J.C. Ottem | timeline score: 18 | |
| Jan 28, 2011 at 21:45 | answer | added | Bruce Reznick | timeline score: 17 | |
| Jan 28, 2011 at 3:27 | history | edited | user2529 | CC BY-SA 2.5 |
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| Jan 27, 2011 at 6:18 | answer | added | Gjergji Zaimi | timeline score: 10 | |
| Jan 27, 2011 at 4:58 | comment | added | user2529 | this still leaves open as to whether a high power of Motzkin's power is a potential answer to my question. | |
| Jan 27, 2011 at 4:43 | comment | added | user2529 | Hi JSE. The proof of that Motzkin's polynomial is not a sum of squares that I know is given by Reznick. This proof is almost brute force. Since the given polynomial is of low degree (deg 6) so the brute force method works. However, raising to high power makes such brute force method difficult. | |
| Jan 27, 2011 at 4:39 | comment | added | JSE | Does Motzkin's proof that his f is not a sum of squares also show that f^N is not a sum of squares for odd N? Or could his polynomial itself already a potential positive answer to your question? | |
| Jan 27, 2011 at 4:08 | history | bounty started | CommunityBot | ||
| Jan 24, 2011 at 12:08 | history | edited | Franz Lemmermeyer | CC BY-SA 2.5 |
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| Jan 24, 2011 at 12:04 | history | asked | user2529 | CC BY-SA 2.5 |