Timeline for Nonnegativity conditions for a polynomial in two variables?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2016 at 10:47 | comment | added | Dima Pasechnik | @hhh : indeed, Polya is for checking strict positivity, not nonnegativity. | |
| Jul 23, 2016 at 16:28 | comment | added | hhh | Yes but is Polya's theorem to check for positive polynomials? Not for non-negative polynomials? Perhaps you know the answer to this here where I am confused which theorem to use? | |
| Sep 23, 2014 at 19:03 | comment | added | Dima Pasechnik | for bivariate polynomials the much better route is outlined in my answer. | |
| Sep 22, 2014 at 14:10 | comment | added | Igor Rivin | @PeterMueller Yes, of course, I wasn't thinking (then you are in the orthant in $\mathbb{R}^3.$) The tricky part with all these algorithms is that they are much better at detecting positivity than non-negativity (see the Powers and Reznick paper - their bounds, which look a little horrible at times, are actually sharp, unfortunately). | |
| Sep 22, 2014 at 14:06 | comment | added | Peter Mueller | By homogenizing the polynomial, that is, considering $Z^4P(X/Z,Y/Z)$, you can apply Polya in the inhomogeneous case as well. | |
| Sep 22, 2014 at 2:13 | vote | accept | Dan Ismailescu | ||
| Sep 22, 2014 at 0:39 | history | answered | Igor Rivin | CC BY-SA 3.0 |