Re: numbpart(k, {a = k})

On 2026-04-18 12:18, Bill Allombert wrote:
 > On Fri, Apr 17, 2026 at 04:50:05PM +0200, Ruud H.G. van Tol wrote:
 >> On 2026-04-17 12:03, Bill Allombert wrote:
 >>> On Fri, Apr 17, 2026 at 08:55:23AM +0200, Ruud H.G. van Tol wrote:

 >>>> Would a variant numbpart(k, {a = k}) be interesting, like Maple has?
 >>>> With the optional a-parameter like with partitions(k, {a = k}, {n 
= k}).
 >>> numbpart use Rademacher formula, which is much faster than 
#partitions(n) but is
 >>> only valid for partitions(n,,).
 >>> I do not know fast formula for the other cases.
 >>>
 >>> For example pari can compute numbpart(1000000) in 5 ms
 >>
 >> I presumed that it would become an additional GEN numbpart_GG(GEN k, 
GEN a).
 >
 > You can write it in GP in one line:
 >
 > nbpart(k,a=k,n=k)=my(s=0);forpart(x=k,s++,a,n);s;

Sure, but that wouldn't tickle my performance bone.

I want to dig into it some more, soon, but am not in a hurry.

-- Ruud