Timeline for Implementing the Farey sequence efficiently
Current License: CC BY-SA 3.0
32 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2023 at 16:53 | answer | added | pseudo determinist | timeline score: 2 | |
| Nov 22, 2018 at 8:23 | answer | added | bill s | timeline score: 5 | |
| May 7, 2013 at 19:06 | vote | accept | user76568 | ||
| May 7, 2013 at 18:57 | history | edited | user76568 | CC BY-SA 3.0 |
deleted 45 characters in body
|
| May 7, 2013 at 18:56 | answer | added | KennyColnago | timeline score: 8 | |
| May 7, 2013 at 18:45 | vote | accept | user76568 | ||
| May 7, 2013 at 19:06 | |||||
| May 7, 2013 at 13:24 | answer | added | Michael E2 | timeline score: 7 | |
| May 7, 2013 at 13:04 | comment | added | Michael E2 | Yes, perhaps you should clarify whether you want an efficient way to generate the Farey sequences or to be shown how to implement certain properties. | |
| May 7, 2013 at 7:07 | comment | added | user76568 | @MichaelE2 you are absolutely correct. Your comment is Superior. :) Do you think I should remake the question? So It'll be Superior? This Farey sequence is packed with logic/rules and confinments, up to a point where I think it can be implmented on/by pure logic :) | |
| May 7, 2013 at 2:35 | comment | added | Michael E2 | I think the problem with finding a recursive solution using the cited property is that the property is not strictly speaking a recurrence relation, since $D_k$ depends on $F_k$. Indeed for any $F_{k-1}$, there are infinitely many solutions for $F_k$ (depending on the order). | |
| May 6, 2013 at 15:56 | vote | accept | user76568 | ||
| May 6, 2013 at 16:00 | |||||
| May 6, 2013 at 12:50 | comment | added | user76568 |
@J.M. Nevertheless, EulerPhi[] can be handy even for our purposes... Along with another 10 (or so) tricks... (as of now) :) Let's start a most efficient Farey competition! The winner.. uumm.. will be awarded a book about Number Theory.. or... candy.
|
|
| May 6, 2013 at 12:39 | comment | added | Dr. belisarius | @J.M. Then I misread it. Sorry. | |
| May 6, 2013 at 12:28 | comment | added | J. M.'s missing motivation♦ |
@bel, that just counts the number of terms in the Farey sequence. That is most easily done in Mathematica, which has EulerPhi[].
|
|
| May 6, 2013 at 12:03 | comment | added | Dr. belisarius | @J.M. Some ideas also here codegolf.stackexchange.com/questions/1896/… | |
| May 6, 2013 at 8:15 | comment | added | bill s |
Right, it holds as long as the denominator is not larger than k -- the DeleteCases in the answer removes those extra ones.
|
|
| May 6, 2013 at 8:14 | comment | added | J. M.'s missing motivation♦ | @bill, there are restrictions to be imposed on the denominators for the constructed mediant to be a proper member of the $k$th Farey sequence, of course. | |
| May 6, 2013 at 8:04 | comment | added | bill s | The mediant property is well known, see for instance: cse.iitd.ernet.in/~mcs103480/farey-icip-100525.pdf | |
| May 6, 2013 at 7:52 | answer | added | bill s | timeline score: 8 | |
| May 6, 2013 at 7:45 | comment | added | user76568 | What you said was not correct, but makes you wonder. | |
| May 6, 2013 at 7:39 | comment | added | bill s | There are many relationships between members of the Farey sequence. For instance, if a/b and c/d are members, then the mediant (a+c)/(b+d) is in the sequence. This property might be easier to exploit than the one you've given. | |
| May 6, 2013 at 7:32 | comment | added | J. M.'s missing motivation♦ | Be my guest, then. :) | |
| May 6, 2013 at 6:34 | comment | added | user76568 | @J.M. I'm sure there is a more elegant, more efficient, simpler to read and comprehend, method. Better than all those mentioned, because it is all very simple. I'll give it a go with a rit or 2 later.... :P | |
| May 6, 2013 at 6:21 | comment | added | bill s | Actually, the OPs code comes from here: physicsforums.com/showthread.php?t=489620 or here demonstrations.wolfram.com/FareySequence whichever came first. | |
| May 6, 2013 at 6:03 | comment | added | J. M.'s missing motivation♦ | Your implementation is certainly simpler. Of course, it's also less efficient. | |
| May 6, 2013 at 5:01 | history | tweeted | twitter.com/#!/StackMma/status/331272590721159168 | ||
| May 6, 2013 at 4:34 | comment | added | user76568 | I saw the implementation in the link. Isn't there a simpler implementation? | |
| May 6, 2013 at 4:30 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
deleted 2 characters in body
|
| May 6, 2013 at 4:23 | comment | added | J. M.'s missing motivation♦ | Hmm... | |
| May 6, 2013 at 4:23 | history | edited | J. M.'s missing motivation♦ |
edited tags
|
|
| May 6, 2013 at 4:17 | history | edited | Szabolcs | CC BY-SA 3.0 |
added 6 characters in body
|
| May 6, 2013 at 3:50 | history | asked | user76568 | CC BY-SA 3.0 |