Timeline for Sandbox for Proposed Challenges
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2020 at 9:03 | history | edited | CommunityBot |
Commonmark migration
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| Sep 17, 2019 at 7:50 | comment | added | Jonathan Frech | I though of something along the lines of \$P[X\neq\mathrm{id}]<\epsilon\$, where \$X\$ models the output and \$\epsilon\$ represents machine accuracy, however on second thought this case is covered by your theoretical surjectivity requirement. | |
| Sep 17, 2019 at 7:43 | comment | added | flawr | @JonathanFrech Can you elaborate how you'd define a Dirichlet distribution over \$SL_n(\mathbb R)\$? I'm not familiar with this distribution and I don't quite see how we can apply it as the support seems to be defined as \$(x_1,\ldots,x_n)\in \mathbb R^n\$ with \$\sum_i x_i =1\$. | |
| Sep 17, 2019 at 7:43 | comment | added | Jonathan Frech | @xnor Even though \$\mathbb{F}_2\$ allows the possibility for bit-fiddling in solutions, possibly being interesting in their own rights. | |
| Sep 17, 2019 at 7:38 | comment | added | Jonathan Frech | "We don't require an uniform distribution." -- would a Dirichlet distribution be allowed? | |
| Sep 14, 2019 at 20:01 | comment | added | xnor | As a side thought, it could be possible to avoid these annoying real-representation issues by changing the challenge to generating integer examples or ones over F_2, but I suspect this won't allow as wide a variety of solutions. | |
| Sep 14, 2019 at 19:53 | comment | added | xnor | I think it would be OK to say that in theory, the output must cover cover the whole space except for some probability-zero subset of it. I see what you're saying about floats being measure zero, but I think this wrinkle is already present and covered by you saying "in theory" and that floating points suffice for reals, so I don't see the change making it more abusable. I also realized that the code probably should be allowed to fail with theoretical probability zero, like if you go the determinant-scaling route, you could get det zero. Maybe defaults cover this already, I'm not sure. | |
| Sep 14, 2019 at 17:49 | comment | added | flawr | @xnor Thanks for you input! This task actually came up when I was trying to test a function I've written and I ended up using the random matirx/scale by determinant solution. I see your point about the zero-probability sets. The only problem I see is that it is hard to define it in a way that cannot be abused: As matrices with floats have only rational entries you could argue that we can only represent a zero-probability set in the first place. (If we use this exact wording.) So I'm not actually sure how to specify this. | |
| Sep 14, 2019 at 7:43 | comment | added | xnor | On second thought, random row operations is probably shorter to golf. And there's probably niftier ways to it like generating the LU decomposition, or taking the exponential of a trace-zero matrix. So this definitely seems like an interesting challenge to golf, at least for languages that don't make it too easy. A technical issue that might be worth addressing is whether it's OK to never be able to generate some probability-zero subset. For instance, what if the method only generates matrices with distinct eigenvalues? I think this should be allowed since floats can't reach everything either. | |
| Sep 14, 2019 at 7:30 | comment | added | xnor | I suspect the interesting solution you have in mind is to start with the identity and do random row operations. But maybe it's shorter to just generate a random matrix and divide the first row by its determinant, even if your language means you need to implement det yourself? | |
| Sep 13, 2019 at 12:41 | history | answered | flawr | CC BY-SA 4.0 |