Talk:Continued fraction/Arithmetic/Construct from rational number: Difference between revisions
Talk:Continued fraction/Arithmetic/Construct from rational number (view source)
Revision as of 11:30, 1 May 2013
, 11 years ago→Using r2cf as Generator a in Continued fraction
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: BTW, Nigel, please use the internal link style for links within Rosetta Code (and <tt>wp:</tt> links for links into english Wikipedia) as that makes for better SEO. It's a small thing, but it's better for this site. Cheers! –[[User:Dkf|Donal Fellows]] 10:01, 5 February 2013 (UTC)
:: IAWTC--[[User:Nigel Galloway|Nigel Galloway]] 13:04, 5 February 2013 (UTC)
::: I've done the first parts of the rename. Any suggestion for what to call the other two pages? Perhaps “<tt>Continued fraction/Arithmetic/Monadic operations</tt>” and “<tt>Continued fraction/Arithmetic/Dyadic operations</tt>”? (Justification: one's a CF->CF operator system, and the other is a CFxCF->CF operator system.) But I'm not very attached to those names. –[[User:Dkf|Donal Fellows]] 11:54, 11 March 2013 (UTC)
:::: Gower uses Bivarate solution for arithmatic with two continued fractions. By extension the case with one continued fraction could be Monovarate. --[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 11:30, 1 May 2013 (UTC)
== Titles are messed up ==
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So perhaps we can just generalize this to a function that just takes a real number. -- [[User:Spoon!|Spoon!]] 22:17, 10 February 2013 (UTC)
: Obviously it is not a problem to add other translations and explore their advantages and limitaions, noting that the results will be language dependant. Note that [[Continued fraction arithmetic/Continued fraction r2cf(Rational N)#1.2F2_3_23.2F8_13.2F11_22.2F7]] calculates the continued fraction for 22/7 as a rational number. [[Continued fraction arithmetic/Continued fraction r2cf(Rational N)#Real_approximations_of_a_rational_number]] demonstrates ever closer approximations of 22/7. The related continued fraction tasks will assume that you generate [3;7] when 22/7 is entered. If you enter 22.0/7 into your Python 'pseudo real' r2cf will you have to do more to interpret your result as [3;7,<math>\infty</math>] which is equivalent? Note that the Perl6 example handles 22/7 correctly, but Perl6 has built into it a Symbolic Maths ability. Compare [[Carmichael 3 strong pseudoprimes, or Miller Rabin's nemesis#Perl_6]] with [[Carmichael 3 strong pseudoprimes, or Miller Rabin's nemesis#Python]] and decide if this comes at a price or if Perl6's use of floor is a mistake. The objective in further tasks will be to calculate <math>\sqrt 2 \times \sqrt 2</math> as 2, which will require understanding the continued fractions as described here. --[[User:Nigel Galloway|Nigel Galloway]] 13:53, 11 February 2013 (UTC)
== Strange series ==
I've just been implementing this and I was looking at the series of numbers leading up to: <math>[314285714;100000000]</math> and I was wondering just what the point of it was. <math>[3141592653589793;1000000000000000]</math> is far more interesting! –[[User:Dkf|Donal Fellows]] 11:42, 10 March 2013 (UTC)
:Never mind me; you're trying for approximations to 22/7 and not actually π. D'oh! –[[User:Dkf|Donal Fellows]] 09:32, 11 March 2013 (UTC)
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