Timeline for Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2018 at 13:25 | comment | added | Aurel | @Oblomov Yes, there is. The corresponding pari/gp command is qfisom (you also have qfauto for automorphisms). | |
| Oct 1, 2018 at 9:34 | answer | added | Davide Cesare Veniani | timeline score: 1 | |
| Jul 22, 2014 at 13:08 | vote | accept | Oblomov | ||
| Jul 22, 2014 at 13:08 | answer | added | Oblomov | timeline score: 9 | |
| Jun 25, 2014 at 20:53 | comment | added | few_reps | @Oblomov Sorry, I have no idea about this ... | |
| Jun 25, 2014 at 13:49 | comment | added | Oblomov | @few_reps: is there an analogous command in pari/gp? (I know that there is an online Magma calculator, but for various reasons, it would be more convenient for me to do it in pari/gp). | |
| Jun 25, 2014 at 3:01 | comment | added | Will Jagy | I think it likely they will have different covering radius. Magma calculates the square of the covering radius, algorithm by G. Nebe. Squares of covering radii add for orthogonal sum, so the radius for $E_8 + E_8$ is just double that for $E_8.$ I will see if this is listed on the Catalogue of Lattices. | |
| Jun 24, 2014 at 14:18 | comment | added | few_reps | Well ... if you have a concrete Gram matrix M, ask Magma ( just enter M and type IsIsometric(LatticeWithGram(M),Lattice("E", 8)+Lattice("E", 8)), the online calculator will do it in few seconds. | |
| Jun 24, 2014 at 12:18 | comment | added | Oblomov | All this seems like a "rather complicated task". I mean: I am in front of a $16 \times 16$ matrix, with not so small integers. Pari/gp can list all 480 minimal length vectors, but analyzing this data will be tedious. I would have hoped for a trick. | |
| Jun 24, 2014 at 11:00 | comment | added | S. Carnahan♦ | Compute some Coxeter diagrams? | |
| Jun 24, 2014 at 9:52 | comment | added | few_reps | It depends on what tools you have ... you could compute the 4th Siegel gamma which distinguishes between these two lattices, or study the graphs of roots (one vertex per root, one edge between two vertices if the corresponding roots are not orthogonal), or compute the automorphism groups, etc... | |
| Jun 24, 2014 at 9:45 | history | asked | Oblomov | CC BY-SA 3.0 |