Re: Looping over ordered partitions

[Aurel Page <aurel.page@normalesup.org>]

    Hi,
    
    On 06/02/2024 17:59, Bill Allombert wrote:
> On Tue, Feb 06, 2024 at 11:46:55AM -0500, Charles Greathouse wrote:
> > The looping commands force and forpart are very convenient. I have a
> > problem I was working on which is looking for the smallest vector (in terms
> > of vecsum) with a certain property. What is the best way to perform such a
> > search in PARI/GP?
> >
> > In my case I have dimension/vector length 11 and sum < 31. (I have an
> > instance with sum 31 but it's probably not optimal.)
> >
> > I can do a forvec, but even forvec(v=vector(11,i,[1,7]), ...) takes a long
> > time (and spends a lot of time looking at values with sum > 30), and I miss
> > instances with numbers larger than 7. Or else I can use forpart but then I
> > need to permute the values (and in my case I definitely have duplicate
> > values, so naive 11! permutations are wasteful and slow).
> >       
> Use forpart + forperm!
>
> forpart(x=30,forperm(x,p,print(p)),,[11,11])
>     
    It does not quite solve your problem because of negative entries,
    but let me mention the existence of enumeration of vectors by
    increasing L1 norm:
    
    ? forvec(v=[0,0,0], if(normlp(v,1)>3,break); print(v))
    
    Cheers,
    Aurel