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

[hermann@stamm-wilbrandt.de]

On 2023-10-02 20:38, hermann@stamm-wilbrandt.de wrote:
> https://reference.wolfram.com/language/ref/PowersRepresentations.html
> "PowersRepresentations[n,k,p]
>     gives the distinct representations of the integer n as
>     a sum of k non-negative p^(th) integer powers."
>
> ...
>
> (wolframscript is free for Raspberry SBCs)
>
> pi@raspberrypi400:~ $ wolframscript
> Wolfram Language 13.3.1 Engine for Linux ARM (64-bit)
> Copyright 1988-2023 Wolfram Research, Inc.
>
> In[1]:= PowersRepresentations[17*29,4,2]
>
> Out[1]= {{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}}
>
> In[2]:=
By the old answer from Bill "foursquares()" is able to give one 
solution, not all.


I did need this again for a current project, and found PARI/GP 
"extern()" solution:

pi@raspberrypi5:~ $ gp -q
? n=17*29;
? extern(strjoin(["wolframscript -code 
\"PowersRepresentations[",Str(n),",4,2]\" | sed 
\"s/{/\[/g;s/}/\]/g\""]))
[[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]]
?


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:~$


Regards,

Hermann.