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Talk:Continued fraction: Difference between revisions
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→Gold Credit for pi and The Harmonic Series: fixed a typo.
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== Related tasks ==
===Thiele interpolation===
One might be [[Thiele's interpolation formula]]. —[[User:Sonia|Sonia]] 21:59, 27 February 2012 (UTC)
:When the structure of the solution: a CF object; generators for aN and bN; and translation from the exact CF object to a real number, is established then we can tackle the Thiele task properly. Note that the cf representation for: arcsin is http://www4b.wolframalpha.com/input/?i=continued%20fraction%20arcsin%28x%29&lk=2; arccos is http://www.wolframalpha.com/input/?i=arcos%28z%29+continued+fraction+representations; and arctan is http://www4b.wolframalpha.com/input/?i=continued%20fraction%20arctan%28x%29&lk=2.
===Moebius function===
I recently read an interesting paper about nested datasets and continued fractions. One of the useful thing that can be done in this regard is to turn a continued fraction into a Moebius function:
http://www.sigmod.org/sigmod/record/issues/0506/p47-article-tropashko.pdf
:<math>a_0 + \cfrac{b_1}{a_1 + \cfrac{b_2}{a_2 + \cfrac{b_3}{a_3 + x}}} = \frac{A_3+B_3x}{C_3+D_3x}</math>
The purpose would be to compute <math>A_n</math>, <math>D_n</math>, <math>C_n</math> and <math>D_n</math> for any n.--[[User:Grondilu|Grondilu]] 00:55, 16 October 2012 (UTC)
As I think about it, I realize there is a recursive property:
:<math>M_n(x) = M_{n-1}(\frac{b_n}{a_n+x})</math>
That should make things much easier than doing the whole algebraic development.
--[[User:Grondilu|Grondilu]] 02:00, 16 October 2012 (UTC)
:Thanks for the reference, using a continued fraction as a sort of index into a tree structure is interesting. Do you intend to implement it?--[[User:Nigel Galloway|Nigel Galloway]] 11:52, 23 October 2012 (UTC)
::I tried with one of my projects [http://github.com/grondilu/libbitcoin-perl on github] but I encountered a few technical difficulties so I put it on hold. I'll go back to it someday.--[[User:Grondilu|Grondilu]] 14:38, 4 November 2012 (UTC)
== creating a continued fraction ==
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<br>on/for true fractions (including whole numbers and improper fractions, including negative fractions),
<br>which would also be a good task for Rosetta Code. -- [[User:Gerard Schildberger|Gerard Schildberger]] 21:03, 24 March 2012 (UTC)
== Gold Credit for pi and The Harmonic Series ==
REXX has already claimed all the extra credits for this task, however for those implementations which can accept a fractional a_series a Gold Credit has been found for demonstrating the relationship between pi and The Harmonic Series:
:<math>\pi/2 = 1 + \cfrac{1}{1 + \cfrac{1}{1/2 + \cfrac{1}{1/3+ \ddots}}}</math>
This was published in American Mathematical Monthly, December 2008 by Dr. Tom Picket, an associate Professor in the Physics Faculty of The University of Southern Indiana.--[[User:Nigel Galloway|Nigel Galloway]] 12:49, 12 September 2012 (UTC)
== Arithmetics?? ==
It's quite complicated, but it can be done. See [http://perl.plover.com/yak/cftalk/ this talk] for instance. A nice library which would hide all the gears behind it would be great. I've never seen any.--[[User:Grondilu|Grondilu]] 00:05, 22 November 2012 (UTC)
== Alternative Perl6 ==
Great to see another view. Follows a screenshot of the code in my browser:
[[File:Perl6.PNG|center|Perl6]]
Is the strange symbol after infix and line 3 an error with the upload, or do I need a special font?--[[User:Nigel Galloway|Nigel Galloway]] 12:57, 3 January 2013 (UTC)
:It's supposed to be the composition operator <math>\circ</math>, which I copied from [[First-class functions#Perl 6]]. It should be a utf8 grapheme. You can replace it with a simple "o".--[[User:Grondilu|Grondilu]] 13:13, 3 January 2013 (UTC)
: A good unicode font will have it. I believe it's part of the set of symbols that were originally in the Symbol font, or maybe one of the *dings fonts. Unicode's full of interesting stuff! (Pity that support for it is still distinctly patchy.) –[[User:Dkf|Donal Fellows]] 15:15, 3 January 2013 (UTC)
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