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 05 '16 at 04:43

score 10 · Answer 1 · answered Dec 04 '16 at 18:51

10

You can view the code for PowersRepresentations using

Needs["GeneralUtilities`"]; 
PrintDefinitions @PowersRepresentations

answered Dec 04 '16 at 18:51

kglr

Can one view codes this way for any function? – Mirko Aveta Dec 04 '16 at 20:46
3

@Mirko, unfortunately, 'PrintDefinitions' does not give the code for Kernel functions; it just returns ''. – kglr Dec 04 '16 at 21:50
@kglr That's because closed-source software hates its users :) – cat Dec 04 '16 at 22:04
@kglr You will find any function is kernel function when you arive v11.2. Even this :) – yode Oct 19 '17 at 11:59
@yode, interesting. – kglr Oct 19 '17 at 12:06

1 Answers1