Timeline for Computation of Galois group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 19, 2014 at 18:00 | vote | accept | SashaP | ||
| May 19, 2014 at 17:15 | answer | added | Jeremy Rouse | timeline score: 4 | |
| May 19, 2014 at 16:25 | comment | added | SashaP | @DavidSpeyer Yes, I know about this method and there are known some error estimates in Chebotarev theorem(so this algorithm is deterministic), but I thought that there are some simple way to distinguish these particular variatns if Galois group. | |
| May 19, 2014 at 16:22 | comment | added | David E Speyer | Lenstra's notes websites.math.leidenuniv.nl/algebra/Lenstra-Chebotarev.pdf are a good introduction to this method. | |
| May 19, 2014 at 16:19 | comment | added | David E Speyer | The practical answer is to reduce $f(x)$ modulo many primes and see if you ever get a factorization of the form $(\mbox{linear})(\mbox{quadratic})(\mbox{quadratic})$. If so, you know that your Galois group contains an element of that cycle structure and so must be $D_5$; by Cebatarov density, if the group is $D_5$, you should see such a factorization for $1/2$ of all primes, so if you don't see one soon you have excellent probabilistic evidence that the group is $C_5$. Finding a provably correct criterion will be messier. | |
| May 19, 2014 at 15:39 | history | asked | SashaP | CC BY-SA 3.0 |