Continued fraction/Arithmetic: Difference between revisions
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→The bivarate solution G(matrix NG, Continued Fraction N1, Continued Fraction N2)
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My description follows [http://perl.plover.com/yak/cftalk/INFO/gosper.txt part of Gosper reproduced on perl.plover.com]. This document is text and unnumbered, you may wish to start by searching for "Addition, Multiplication, etc. of Two Continued Fractions" prior to reading the whole thing.
[http://perl.plover.com/classes/cftalk/TALK/slide001.html perl.plover.com] also includes a series of slides as a class on continued fractions. The example [1;5,2] + 1/2 in [[Continued fraction
For these tasks continued fractions will be of the form:
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so each may be described by the notation [<math>a_0 ; a_1, a_2, ..., a_n</math>]
==[[Continued fraction
During these tasks I shall use the function described in this task to create continued fractions from rational numbers.
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and a function <math>G(\mathrm{matrix}</math> <math>\mathit{NG}, \mathrm{Number}</math> <math>N_1, \mathrm{Number}</math> <math>N_2)</math>
which returns:
: <math>\frac{a_{12}\times N_1\times N_2 + a_1\times N_1 + a_2\times N_2 + a}{b_{12}\times N_1\times N_2 + b_1\times N_1 +
===Basic identities===
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So I can define arithmetic as operations on this matrix which make <math>a_{12}</math>, <math>a_1</math>, <math>a_2</math>, <math>b_{12}</math>, <math>b_1</math>, <math>b_2</math> zero and read the answer from <math>a</math> and <math>b</math>. This is more interesting when <math>N_1</math> and <math>N_2</math> are continued fractions, which is the subject of the following tasks.
==[[Continued fraction
Here we perform basic mathematical operations on a single continued fraction.
==[[Continued fraction
Here we perform basic mathematical operations on two continued fractions.
* Compare two continued fractions
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