Timeline for Existence of solutions of a polynomial system
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2014 at 8:23 | vote | accept | Andrej Bauer | ||
| Aug 5, 2014 at 8:23 | vote | accept | Andrej Bauer | ||
| Aug 5, 2014 at 8:23 | |||||
| Aug 5, 2014 at 0:55 | answer | added | Vladimir Dotsenko | timeline score: 6 | |
| Aug 4, 2014 at 23:00 | answer | added | John Mount | timeline score: 2 | |
| Aug 4, 2014 at 20:26 | history | rollback | Andrej Bauer |
Rollback to Revision 2
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| S Aug 4, 2014 at 20:21 | history | suggested | John Mount | CC BY-SA 3.0 |
make want of an interior solution more prominent
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| Aug 4, 2014 at 20:03 | review | Suggested edits | |||
| S Aug 4, 2014 at 20:21 | |||||
| Aug 2, 2014 at 4:11 | comment | added | Brendan McKay | Always $x_k=1\pm x_0$, so for solutions in $[0,1]^{k+1}$ it must be that $x_k=1-x_0$. This can continue to $x_{k-1}$ and so on, but I don't know how to see that it remains real, let alone in $[0,1]$. | |
| Aug 1, 2014 at 20:54 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
added 65 characters in body
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| Aug 1, 2014 at 16:03 | answer | added | John Mount | timeline score: 3 | |
| Aug 1, 2014 at 13:40 | comment | added | Vít Tuček | Did you try to express $S(p,x)$ in terms of Bernstein basis? Can Mathematica handle that at least for some small $k$? | |
| Aug 1, 2014 at 13:32 | comment | added | Vít Tuček | The polynomial $S(p,x)$ is actually divisible by $p$, which means that we have a well defined mapping $\mathbb{R}^{k+1} \to \mathbb{R}^{k+1}$. This allows us to use topological methods such as this one: en.wikipedia.org/wiki/… | |
| Aug 1, 2014 at 13:09 | comment | added | Vít Tuček | In other words, we have a family of one-sheeted hyperboloids $$ \sum_{i=1}^k {k \choose i} p^{i-1} (1 - p)^{k - i-1}(x_i-p)^2 - \frac{1}{1-p}(x_0-(p-1))^2 = 1 $$ in $\mathbb{R}^{k+1}$ parametrised by $p \in [0,1]$ and we want to know whether there is a point lying in all of them at once. | |
| Aug 1, 2014 at 9:41 | history | asked | Andrej Bauer | CC BY-SA 3.0 |