Talk:Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2): Difference between revisions

: This depends on the definition of the canonical form for negative numbers. 151/77 is [1;1,24,1,2] so the negative form [-1;-1,-24,-1,-2] seems clearer to me. [[Continued_fraction/Arithmetic/Construct_from_rational_number]] defines how to construct continued fractions thus determine: the integer part; and remainder part, of N₁ divided by N₂. It then sets N₁ to N₂ and N₂ to the determined remainder part. It then outputs the determined integer part. It does this until abs(N₂) is zero. Here N₁ is -151 and N₂ is 77. -151/77 is -1 remainder -74. Wikis seem to define the canaonical form as [a₀;a_i,...,a_j] where a₀ is an integer and a_i,...,a_j are positive integers. [http://www.andrewduncan.ws/goldenratio/continuedfractions/index.html] gives [-2 ; 25,1,2,1705908949761,1,1,4,2,1,4,1,23…] so your version has some support, but if we adopt it then Mathmatica will have to be rewritten and I think the form which makes the negative form similar to the positive form is better.--[[User:Nigel Galloway|Nigel Galloway]] 13:36, 11 March 2013 (UTC)