Talk:Continued fraction/Arithmetic/G(matrix ng, continued fraction n): Difference between revisions

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Thundergnat moved page Talk:Continued fraction/Arithmetic/G(matrix NG, Contined Fraction N) to Talk:Continued fraction/Arithmetic/G(matrix ng, continued fraction n): Follow normal task title capitalization policy

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Revision as of 10:25, 9 July 2015 (view source) Rdm (talk \| contribs) (→‎Marking as "draft": new section) ← Older edit		Latest revision as of 14:00, 7 November 2020 (view source) Thundergnat (talk \| contribs) m (Thundergnat moved page Talk:Continued fraction/Arithmetic/G(matrix NG, Contined Fraction N) to Talk:Continued fraction/Arithmetic/G(matrix ng, continued fraction n): Follow normal task title capitalization policy)
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Line 5: I can't get the c++ entry to compile. How is that done? --[[User:Rdm\|Rdm]] ([[User talk:Rdm\|talk]]) 14:05, 8 July 2015 (UTC) : Answer: : * Replace reference to NG_8 with NG_4 : * Take the first body of code and save it as ng.hpp - adding these lines at the top <lang c++>#include <iostream> #include <cmath> #include "r2cf.hpp"</lang> : * populate r2cf.hpp with the first block of code at [[Continued_fraction/Arithmetic/Construct_from_rational_number#C.2B.2B]] : Each main block gets an <code>#include "ng.hpp"</code> header and gets compiled as c++11 : I think the implementation should be fixed up so it works, but I'll leave that to someone else... --[[User:Rdm\|Rdm]] ([[User talk:Rdm\|talk]]) 04:32, 10 July 2015 (UTC) == Marking as "draft" == Line 11 ⟶ 22: Also, currently: * The task description uses notation [1;3,5] and [3;7] but this notation does not appear in any of the implementations (well, in some as a literal string, but it is not used for computational purposes). This is either a red herring or needs documentation. Perhaps it's a reference into some external manuscript? Or perhaps it has to do with a method for constructing continued fractions? Whatever is going on should be stated more clearly. * The task description uses the notation "+ 1/2" which apparently corresponds to an "NG matrix" with a1=2, a=1, b1=0, b=2 and the notation "divided by 4" which apparently corresponds to an "NG matrix" with a1=1, a=0, b1=0, b=4. There is probably a good reason for this, but that should also be documented. Some implementations also use other "NG Matrices" but why? * It's not at all clear how we would compute an arithmetic geometric mean in this task. We would need to be able to compute the square root of an arbitrary value, but most square root algorithms (including continued fraction expansion) would require we be able to multiply two continued fractions if we are to compute the square root of a number represented as a continued fraction. The best we can do here is find a fixed precision rational value for use in an NG4 matrix and combine that with a continued fraction. But if we are going to do that, we might as well stick with rational approximations for the entire algorithm. * The task mentions generating an Arithmetic-geometric mean but neglects to mention what this would be a mean of. * The task mentions the expression <math>\frac{1 + \frac{1}{\sqrt{2}}}{2}</math> but none of the implementations use that expression, nor does a continued fraction expression representing that value (such as 0 1 5 1 4 1 4 1 4 1 4 1...) seem to appear in the current implementations. Some implementations include a continued fraction for <math>\frac{1 + \sqrt{2}}{2}</math> but that's not the same (similar, but different). Anyways... this draft has potential, but it also needs some work. --[[User:Rdm\|Rdm]] ([[User talk:Rdm\|talk]]) 10:25, 9 July 2015 (UTC)

Talk:Continued fraction/Arithmetic/G(matrix ng, continued fraction n): Difference between revisions

Talk:Continued fraction/Arithmetic/G(matrix ng, continued fraction n) (view source)

Revision as of 14:00, 7 November 2020