Timeline for Sign of an integer polynomial at a real algebraic number
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 25, 2019 at 23:41 | comment | added | Arnaldo Mandel | Thank you, the reference has it! | |
| Sep 25, 2019 at 19:45 | comment | added | Emil Jeřábek | Yes, there are fairly simple algorithms. I suggest you study Lecture VII (Sturm theory) in Chee K. Yap, Fundamental problems in algorithmic algebra. | |
| Sep 25, 2019 at 18:51 | comment | added | Benoît Kloeckner | @GreginGre: I do not get your comment. Certainly when $r$ (or $a$, why the change of notation?) is an integer, then we can compute $f(a)$ exactly, it is an integer and its sign is no mystery. When $r$ is a general algebraic number seems another matter. | |
| Sep 25, 2019 at 18:37 | comment | added | GreginGre | Mmmmh, I don't understand which role $p$ is playing. Taking an arbitrary $a\in \mathbb{Z}$ and setting $p=(X-a)^{n+1}$, we see that in this case your question becomes: let $f\in \mathbb{Z}[x]$ of degree $\leq n$. Find out the sign of $f(a)$ using exact arithmetic...Do you know algorithms for this particular question ? | |
| Sep 25, 2019 at 18:12 | history | asked | Arnaldo Mandel | CC BY-SA 4.0 |