Re: Missing functionality in forvec()

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Jan 24, 2024 at 01:19:28AM -0800, Ilya Zakharevich wrote:
> I want to use forwec() in a complicated algorithms needing a lot of
> cached data.  The caches should be recalculated on backtracking.

I agree, forvec is nice for interactive use, but it does not lend itself
to efficient code, because you have to recompute evrything from scratch
for each entries.

I used cache and backtracking to extrem length in my thesis.
(e.g. the libpari function testpermutation)

>   Here I consider forvec() as if it is traversing-in-order an “ordered rooted tree”.
> 
> While forvec() takes a lot of workload under the cover, with forvec()
> it is a PITA to detect backtracking.  On the other hand, I can see
> that with an extra argument taking an (optional) variable reference
> 'v, and reporting the details of backtracking in v, the life would be
> much easier!
> 
> The docs could go like this (I would need only one of these 3 flavors
> of reporting; two others are added in anticipation of usability in
> other situations):
> 
>   Let n be the number of tail counters which wrapped around after the
>   preceding iteration, and m be the number which will wrap around on
>   the next iteration.  If 'v was a small/v/vector at start, put n and
>   m into the first two components; otherwise report n or -m,
>   preferring the non-0 value.  (For what follows, note that with
>   flag=2 both n and m may be non-0 even if the trailing ranges are not
>   of length 1.)  If 'v was 0 at start, prefer the largest of n and m,
>   otherwise prefer positive or negative depending on the sign of 'v at
>   start.

Could you give an example of usage ?

Maybe print all the numbers of the form x^2+2*x^2+3*x^2+...+n*x^2 ?

I was considering suggesting the number of way to write a number as a sum of k
squares using the naive algorithm, but this require the ability to cut branches.

I am concerned the interface would be too complex to be of use.

Cheers,
Bill.