Continued fraction/Arithmetic: Difference between revisions
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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. |
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. |
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[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 |
[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/Arithmetic/G(matrix NG, Contined Fraction N) | G(matrix NG, Contined Fraction_N)]] is worked through in this class. |
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For these tasks continued fractions will be of the form: |
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>] |
so each may be described by the notation [<math>a_0 ; a_1, a_2, ..., a_n</math>] |
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==[[Continued fraction |
==[[Continued fraction/Arithmetic/Construct from rational number]]== |
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During these tasks I shall use the function described in this task to create continued fractions from rational numbers. |
During these tasks I shall use the function described in this task to create continued fractions from rational numbers. |
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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. |
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. |
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==[[Continued fraction |
==[[Continued fraction/Arithmetic/G(matrix NG, Contined Fraction N) | G(matrix NG, Contined Fraction N)]]== |
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Here we perform basic mathematical operations on a single continued fraction. |
Here we perform basic mathematical operations on a single continued fraction. |
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==[[Continued fraction |
==[[Continued fraction/Arithmetic/G(matrix NG, Contined Fraction N1, Contined Fraction N2) | The bivarate solution G(matrix NG, Continued Fraction N<sub>1</sub>, Continued Fraction N<sub>2</sub>)]]== |
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Here we perform basic mathematical operations on two continued fractions. |
Here we perform basic mathematical operations on two continued fractions. |
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* Compare two continued fractions |
* Compare two continued fractions |
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