How does Mathematica compute how to write integers as the sum of k non-negative pth integer powers so quickly?

Question

"PowersRepresentations[n,k,p] gives the distinct representations of the integer n as a sum of k non-negative p-th integer powers"

How does Mathematica do this computation so quickly? Is there a fast algorithm? What is it?

I am particularly interested in the case where $n$ is the sum of $k$ squares of positive integers.

There is a little man inside the computer who is good at sums — wolfies, Dec 5, 2016 at 4:43

kglr · Accepted Answer · 2016-12-04 18:51:26Z

10

You can view the code for PowersRepresentations using

Needs["GeneralUtilities`"]; 
PrintDefinitions @PowersRepresentations

answered Dec 4, 2016 at 18:51

kglr

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$\begingroup$ Can one view codes this way for any function? $\endgroup$
– Mirko Aveta
Dec 4, 2016 at 20:46
3

$\begingroup$ @Mirko, unfortunately, 'PrintDefinitions' does not give the code for Kernel functions; it just returns '<Kernel Function>'. $\endgroup$
– kglr
Dec 4, 2016 at 21:50
$\begingroup$ @kglr That's because closed-source software hates its users :) $\endgroup$
– cat
Dec 4, 2016 at 22:04
$\begingroup$ @kglr You will find any function is kernel function when you arive v11.2. Even this :) $\endgroup$
– yode
Oct 19, 2017 at 11:59
$\begingroup$ @yode, interesting. $\endgroup$
– kglr
Oct 19, 2017 at 12:06

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