hermann on Wed, 04 Oct 2023 02:25:45 +0200


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

On 2023-10-03 10:45, Bill Allombert wrote:


Is qfsolve() only available for GP?


Of course not:

? ??qfsolve
qfsolve(G):
...
   The library syntax is GEN qfsolve(GEN G).


Thanks Bill, so I have to search for "The library syntax" in either
GP user manual (more than 1000 matches) or "??func" output.

I implemented foursquare.cc gist, nice libpari hands-on:
https://gist.github.com/Hermann-SW/fc96e5b1148c72ce07cfa4e55b6c0cd3

Using C++ does not change the qfsolve runtime, no surprise.

? p=precprime(10^30)
%41 = 999999999999999999999999999989
? q=precprime(p-1)
%42 = 999999999999999999999999999983
? n=p*q
%43 = 999999999999999999999999999972000000000000000000000000000187
? foursquare(n)
%44 = [312403411064839129238661430583, 892113694587116093864238410176, 253468622571348560165608955929, 205647567593108547766440174091]~ 
? ##
  ***   last result computed in 2,769 ms.
?


libgmpxx+lipbari:

$ f=foursquare
$ g++ $f.cc -lgmp -lgmpxx -O3 -o $f -lpari -DPARI -Wall -Wextra -pedantic 
$ ./$f 999999999999999999999999999989 999999999999999999999999999983
R = qfsolve(M)
2.85703s
223605138439657340220247124809 147944036070869714718268156597 314020169936458430849348767399 910771451642793118995923538064 
sum of 4 squares verified for 61-digit number
$


Regards,

Hermann.