prism-magma.html

<h2>Full example</h2>
<pre><code>// Source: http://magma.maths.usyd.edu.au/magma/handbook/text/115#963
> D := Denominator;
> N := Numerator;
> farey := function(n)
>    f := [ RationalField() | 0, 1/n ];
>    p := 0;
>    q := 1;
>    while p/q lt 1 do
>       p := ( D(f[#f-1]) + n) div D(f[#f]) * N(f[#f])  - N(f[#f-1]);
>       q := ( D(f[#f-1]) + n) div D(f[#f]) * D(f[#f])  - D(f[#f-1]);
>       Append(~f, p/q);
>    end while;
>    return f;
> end function;
> function farey(n)
>    if n eq 1 then
>       return [RationalField() | 0, 1 ];
>    else
>       f := farey(n-1);
>       i := 0;
>       while i lt #f-1 do
>          i +:= 1;
>          if D(f[i]) + D(f[i+1]) eq n then
>             Insert( ~f, i+1, (N(f[i]) + N(f[i+1]))/(D(f[i]) + D(f[i+1])));
>          end if;
>       end while;
>       return f;
>    end if;
> end function;
> farey := func&lt; n |
>               Sort(Setseq({ a/b : a in { 0..n }, b in { 1..n } | a le b }))>;
> farey(6);
[ 0, 1/6, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 1 ]</code></pre>