Timeline for homogeneous polynomials with suitable number of variables that has a non-trivial solution
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2011 at 10:24 | comment | added | Ehsan M. Kermani | Dustin Cartwright: Thanks for your complete answer. That is a careful point. | |
| Mar 17, 2011 at 18:30 | comment | added | Dustin Cartwright | With respect to 4, I'll add that if your equations are real, homogeneous, of odd degree, and there are more variables than equations, then there is a non-trivial real solution. By adding linear equations, you can assume that there is one more variable then equation. Bezout's theorem says that generically, the number of complex solutions in projective space will be the product of the degrees, which is odd. Since the non-real solutions come in complex conjugate pairs, there must be a real solution. For non-generic equations, you can always approximate by generic systems. | |
| Mar 17, 2011 at 15:32 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
added 303 characters in body
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| Mar 17, 2011 at 10:22 | vote | accept | Ehsan M. Kermani | ||
| Mar 17, 2011 at 9:49 | comment | added | Ehsan M. Kermani | For 1) yes, definitely, I meant a consistent set of equations. For the first line of my question I intended to give the background in a few words. | |
| Mar 17, 2011 at 7:41 | history | answered | Sándor Kovács | CC BY-SA 2.5 |