Farey sequence: Difference between revisions
Add MATLAB implementation
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{3045, 12233, 27399, 48679, 76117, 109501, 149019, 194751, 246327, 304193}</pre>
=={{header|MATLAB}}==
{{trans|Kotlin}}
<syntaxhighlight lang="MATLAB">
clear all;close all;clc;
% Print Farey sequences for 1 to 11
for i = 1:11
farey_sequence = farey(i);
fprintf('%2d: %s\n', i, strjoin(farey_sequence, ' '));
end
fprintf('\n');
% Print the number of fractions in Farey sequences for 100 to 1000 step 100
for i = 100:100:1000
farey_sequence = farey(i);
fprintf('%4d: %6d fractions\n', i, length(farey_sequence));
end
function farey_sequence = farey(n)
a = 0;
b = 1;
c = 1;
d = n;
farey_sequence = {[num2str(a) '/' num2str(b)]}; % Initialize the sequence with "0/1"
while c <= n
k = fix((n + b) / d);
aa = a;
bb = b;
a = c;
b = d;
c = k * c - aa;
d = k * d - bb;
farey_sequence{end+1} = [num2str(a) '/' num2str(b)]; % Append the fraction to the sequence
end
end
</syntaxhighlight>
{{out}}
<pre>
1: 0/1 1/1
2: 0/1 1/2 1/1
3: 0/1 1/3 1/2 2/3 1/1
4: 0/1 1/4 1/3 1/2 2/3 3/4 1/1
5: 0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1
6: 0/1 1/6 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/6 1/1
7: 0/1 1/7 1/6 1/5 1/4 2/7 1/3 2/5 3/7 1/2 4/7 3/5 2/3 5/7 3/4 4/5 5/6 6/7 1/1
8: 0/1 1/8 1/7 1/6 1/5 1/4 2/7 1/3 3/8 2/5 3/7 1/2 4/7 3/5 5/8 2/3 5/7 3/4 4/5 5/6 6/7 7/8 1/1
9: 0/1 1/9 1/8 1/7 1/6 1/5 2/9 1/4 2/7 1/3 3/8 2/5 3/7 4/9 1/2 5/9 4/7 3/5 5/8 2/3 5/7 3/4 7/9 4/5 5/6 6/7 7/8 8/9 1/1
10: 0/1 1/10 1/9 1/8 1/7 1/6 1/5 2/9 1/4 2/7 3/10 1/3 3/8 2/5 3/7 4/9 1/2 5/9 4/7 3/5 5/8 2/3 7/10 5/7 3/4 7/9 4/5 5/6 6/7 7/8 8/9 9/10 1/1
11: 0/1 1/11 1/10 1/9 1/8 1/7 1/6 2/11 1/5 2/9 1/4 3/11 2/7 3/10 1/3 4/11 3/8 2/5 3/7 4/9 5/11 1/2 6/11 5/9 4/7 3/5 5/8 7/11 2/3 7/10 5/7 8/11 3/4 7/9 4/5 9/11 5/6 6/7 7/8 8/9 9/10 10/11 1/1
100: 3045 fractions
200: 12233 fractions
300: 27399 fractions
400: 48679 fractions
500: 76117 fractions
600: 109501 fractions
700: 149019 fractions
800: 194751 fractions
900: 246327 fractions
1000: 304193 fractions
</pre>
=={{header|Maxima}}==
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