Timeline for Implementing the Farey sequence efficiently
Current License: CC BY-SA 3.0
16 events
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| May 6, 2013 at 16:11 | comment | added | user76568 | @bills Aaaaaaaaaand, I do VERY MUCH seriously thank you for the time you spent on my question, and the new tricks I learned from your implementation. :) | |
| May 6, 2013 at 16:04 | comment | added | user76568 | @bills Well, obviously. Regarding that, I don't think It's TOO weird, that initially I was hoping for a step up in performance. By the way, it isn't much slower... It's same'ish-- :) | |
| May 6, 2013 at 16:00 | comment | added | bill s |
@dror - It is interesting that the functional answer is so much slower than the "simple" answer. Maybe it's because the very basic commands like Union and Table are quicker than comparatively obscure commands like Numerator and DeleteCases.
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| May 6, 2013 at 15:56 | vote | accept | user76568 | ||
| May 6, 2013 at 16:00 | |||||
| May 6, 2013 at 14:17 | comment | added | user76568 | @MarkMcClure , I guess you are right. Obviously, the performance is more than "enough" and the recovery of Stern-Brocot tree obtained by merely removing the head is quite nice. Though, I know there are many many mathematical facts that could be harnessed, for the sake of elegance, simplicity, readability (and performance!!!) among others, while still maintaining functional form.. I actually am inclined to implement it... But I don't have time now. | |
| May 6, 2013 at 13:32 | comment | added | Mark McClure |
@Dror Well, you did ask for a functional approach and this certainly provides it. Also, you never indicated that speed was your primary concern and I see no immediate reason that it should be. The primary advantage of this approach that I see is the clarity provided by its immediate connection to the mediant. By removing the DeleteCases step, for example, we essentially recover the Stern-Brocot tree.
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| May 6, 2013 at 9:25 | comment | added | user76568 | This implementation is slowest thus far as far as I can check | |
| May 6, 2013 at 8:57 | comment | added | user76568 | I'll do some performance testing on this marble. Though I'm working on one my self.... | |
| May 6, 2013 at 8:46 | comment | added | J. M.'s missing motivation♦ | Well, the OP did dismiss my proposal so glibly... | |
| May 6, 2013 at 8:33 | comment | added | bill s | That's good, but you know, this whole approach doesn't seem any faster than the simple way! | |
| May 6, 2013 at 8:30 | history | edited | bill s | CC BY-SA 3.0 |
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| May 6, 2013 at 8:29 | comment | added | J. M.'s missing motivation♦ |
med[v_List] := Total[Numerator[v]]/Total[Denominator[v]] is a bit more compact.
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| May 6, 2013 at 8:23 | history | edited | bill s | CC BY-SA 3.0 |
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| May 6, 2013 at 8:07 | history | edited | bill s | CC BY-SA 3.0 |
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| May 6, 2013 at 8:02 | history | edited | bill s | CC BY-SA 3.0 |
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| May 6, 2013 at 7:52 | history | answered | bill s | CC BY-SA 3.0 |