Re: How to generate wolframscript "PowersRepresentations[...]" output in PARI/GP

[hermann@stamm-wilbrandt.de]

On 2024-03-11 15:30, hermann@stamm-wilbrandt.de wrote:
> ...
> While wolframscript is free on Raspberry computers, a license is
> needed for other computers. So I implemented "it" from scratch in
> PARI/GP to have no dependency. With "it" I mean I implemented for p=2
> only, and renamed accordingly. It creates unique entries with
> non-negative non-decreasing values:
>
> hermann@7950x:~$ cat SquaresRepresentations.gp
> SquaresRepresentations(n,k,a=0)={
>   my(R=List(),m=sqrtint(n\k));
>   if(k==1,return(if(m>=a&&n==m^2,[m],[])));
>   
> for(b=a,m,foreach(SquaresRepresentations(n-b^2,k-1,b),s,listput(R,concat([b],s))));
>   Vec(R);
> }
>
> n=eval(getenv("n"));
> print(SquaresRepresentations(n,4));
> hermann@7950x:~$
>
> hermann@7950x:~$ n=17*29 gp -q < SquaresRepresentations.gp
> [[0, 0, 3, 22], [0, 0, 13, 18], [0, 4, 6, 21], [0, 5, 12, 18], [1, 2,
> 2, 22], [1, 10, 14, 14], [2, 2, 14, 17], [2, 5, 8, 20], [2, 8, 8, 19],
> [2, 8, 13, 16], [2, 10, 10, 17], [3, 4, 12, 18], [3, 12, 12, 14], [4,
> 4, 10, 19], [4, 5, 14, 16], [4, 10, 11, 16], [6, 6, 14, 15], [6, 12,
> 12, 13], [8, 8, 13, 14]]
> hermann@7950x:~$
I enhanced above script and made it a gist with version control:
https://gist.github.com/Hermann-SW/18423ac08eda224dd06683883c7b10ac

Above output gave all non-negative monotonic increasing sums of k 
squares (≥a).
Gist allows to return all (signed+permuted) versions as in addition.
Or only the count of all determined sums of k squares, which is r_k(n).

In case k==3, sum of 3 squares function for n
https://en.wikipedia.org/wiki/Sum_of_squares_function#k_=_3

is asserted to be the count determined by script (for verification).

Regards,

Hermann.