Timeline for Existence of non-trivial solution to non linear polynomial system
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2013 at 3:02 | review | First posts | |||
| Jun 26, 2013 at 10:33 | |||||
| Jun 16, 2013 at 18:47 | comment | added | user34985 | I didn't unerstand- why the first conic must have one rational point and how can I parametrise it. Can you please give an example? | |
| Jun 15, 2013 at 21:46 | answer | added | Dietrich Burde | timeline score: 3 | |
| Jun 14, 2013 at 20:11 | comment | added | Jérémy Blanc | Your equations define conics in $\mathbb{P}^2$, so you always have solutions, at least over an algebraically closed field. In general you will find $4$ points, but it could be less in particular cases if the curves intersect with tangency. If you want to work over the field of reals (which seems to be because of inequalities), then your first conic need to have at least one point, in which case it is rational, so you can parametrise and obtain a polynomial in degree $4$. | |
| Jun 14, 2013 at 19:20 | history | asked | user34985 | CC BY-SA 3.0 |