Timeline for Checking a generating set of $\mathbb{Z}^k$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2017 at 11:44 | answer | added | Jan-Christoph Schlage-Puchta | timeline score: 0 | |
| Oct 9, 2017 at 23:11 | comment | added | user6976 | @DavidHandelman: I had the same idea (see my answer). But this does not seem much easier than the Smith normal form because the GCD is the largest diagonal element of the Smith form. | |
| Oct 9, 2017 at 22:45 | comment | added | David Handelman | Take the gcd of all the determinants of the square matrices coming from $k$ vectors at a time. This will be 1 iff the set generates the standard copy of ${\bf Z}^k$. Worst possible case is that $n$ choose $k$ subsets will be required, but if it is a generating set, far fewer subsets should be required. | |
| Oct 9, 2017 at 17:02 | answer | added | user6976 | timeline score: 0 | |
| Oct 9, 2017 at 0:20 | answer | added | Richard Stanley | timeline score: 9 | |
| Oct 8, 2017 at 23:57 | history | asked | Mikhail Tikhomirov | CC BY-SA 3.0 |