Timeline for Database of integer edge lengths that can form tetrahedrons
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2017 at 20:23 | comment | added | Stefan Kohl♦ | The computations are with integers, so are exact. | |
| Oct 1, 2017 at 20:14 | comment | added | Peter Heinig | [..] Of course, it is not clear at all what this logically implies for the complexity of the problem in the OP; after all, it's not clear that one must compute a Cayley-Menger determinant. That's only one algorithm in a countably-infinite set of possible algorithms. | |
| Oct 1, 2017 at 20:13 | comment | added | Peter Heinig | Of course, if GAP uses some 'exact arithmetic', then, ideally, assuming we believe GAP, numerics should not be an issue, but it is scientifically very valuable to simply take a skeptical/verificationist/Bayesian stance and pretend we only believe what we see sufficiently often independently-reproduced. Also, it may be relevant for the complexity-theoretic 'status' of the OP that the 'problem' of computing $\det\colon\bigcup_{n\in\omega}\mathbb{Z}^{n\times n}\to\mathbb{Z}$, $A\mapsto\det(A)$ has been proved to be GapL-complete. [...] | |
| Oct 1, 2017 at 20:11 | comment | added | Peter Heinig | [..], no 'externalization' needed, and without bloating the thread. You could, if so inclined, simply use some script to automatically generate a markup-code using a matrix-environment and some {\tiny\text{}} hackery, and then the couple of hundred values should easily fit in a reasonably small space. Why so much care? As Joseph Malkevitch reminded us of, if the machine displays a small positive value, one should be suspicious whether this is a 'false positive' (pun), in the sense that the true determinant value is zero, but numerical errors make it seem otherwise,[..] | |
| Oct 1, 2017 at 20:08 | comment | added | Peter Heinig | It would be even better an addition to this thread if (0) the method used by GAP to compute 'DeterminantMat' would be named, with a reference/testimonies of practitioners, (1) you re-computed it with GAP's 'DeterminantMatDivFree' routine, which allegedly uses a division-free algorithm published in Meena Mahajan V. Vinay 1997 (2) all the computed values for these determinants were listed here, both for the 'DeterminantMat'- and the 'DeterminantMatDivFree'-run. I think that it is easy and desirable to do this in-thread,[...] | |
| Oct 1, 2017 at 16:47 | history | answered | Stefan Kohl♦ | CC BY-SA 3.0 |