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Engel expansion: Difference between revisions
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Engel expansion: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 33, 33, 35, 58, 62, 521, 3125] (34 components)
Back to rational: 25.628906
</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
engel_encode(x) := block (
[a:[]],
while(x > 0) do (
ai: ceiling(1/x),
x: x*ai - 1,
a: append(a, [ai])
),
return(a)
);
engel_decode(a) := block (
[x:0, my_product:1],
for ai in a do (
my_product: my_product*ai,
x: x + 1/(my_product)
),
return(x)
);
</syntaxhighlight>
{{out}}
<pre>
engel_encode(3.14159265358979);
[1,1,1,8,8,17,19,300,1991,2767,8641,16313,1628438,7702318,25297938,431350188,765676622,776491263,1739733589,2329473788,6871947674,17179869184]
engel_decode(%);
7074237752028433/2251799813685248
engel_encode(2.71828182845904);
[1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,60,89,126,565,686,1293,7419,13529,59245,65443,133166,225384,655321,656924,2365071,2618883,5212339,107374183,178956971,536870912]
engel_decode(%);
3060513257434031/1125899906842624
engel_encode(1.414213562373095);
[1,3,5,5,16,18,78,102,120,144,277,286,740,38370,118617,120453,169594,5696244,6316129,10129640,67108864]
engel_decode(%);
1592262918131443/1125899906842624
</pre>
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