Re: choosing k elements from a "set", and concat of vecsmall

Thanks for the thoughtful reply and explanation.

On Wed, Jul 2, 2025, 4:57 PM Karim Belabas <[email protected]>
wrote:

> * Hans L [2025-07-02 22:33]:
> > I often have a need to loop over all "n choose k" elements from a set.
> The
> > closest builtin functionality I have found for this  is to use forsubset,
> > and then build a vector from that with vector as follows:
> >
> > forsubset([#S,k], s0,
> >   my(s = vector(k, i, S[s0[i]]));
> >   ...
> > );
> >
> > Is there any more appropriate/efficient way to do such a thing?  It
> seems a
> > little convoluted and odd to me that forsubset can't optionally accept a
> > vector as input.
>
>  forsubset([#S,k], s0,
>    my(s = vecextract(S, s0));
>    ...
>  );
>
> > Another somewhat related thing I noticed recently which feels like an
> > oversight is when that concat is presented with a t_VEC and t_VECSMALL,
> it
> > just inserts the t_VECSMALL as a single element.
>
> It's not an oversight. There is an ambiguity about what "converting x to
> a vector" means and I chose the simplest definition: not Vec(x) but
> simply [x].
>
> In particular, concat([1,2,3], 4*t + 5) returns concat([1,2,3, 4*t + 5])
> and not [1,2,3,4,5] (N.B. Vec(4*t+5) = [4,5].)
>
> The concat function is hard to describe completely and ??concat only
> tells part of the story.
>
> 0)concat(x, y) works "as expected" when x and y have the same type.
>
> It should probably have been left that way, requiring explicit type
> coercions throughout to avoid ambiguities and surprising behavious.
> Unfortunately, but in agreement with PARI philosophy, I have overloaded
> it for convenience a long time ago, which made is somewhat "surprising".
>
> 1) There are special rules when either x or y is a t_MAT, t_LIST or t_STR:
> we convert the other argument to the relevant type and concat as before.
> (in particular, concat([1,2], "x") is "[1, 2]x" and not [1, 2,"x"] !)
>
> We don't do this for t_VECSMALL: it's in general not possible to convert
> the other element to a word-sized integer type fitting in a t_VECSMALL.
>
> 2) A "vector type" is defined as t_VEC or t_COL. concat(v, x), when v is
> a vector type but x is not, converts x to the type of v in the above
> sense ([x] or [x]~), then concatenates. More simply, it appends x to v.
>
> It indeed follows that concat(v, t_VECSMALL) appends the t_VECSMALL to v.
>
> Rationale for t_VECSMALL not being a vector type: a vector is either for
> linear algebra or a collection of arbitrary objects. t_VECSMALL are
> neither. In most cases, they arise as permutations or partitions, and
> are viewed as an atomic object and not as a collection of integers.
>
> 3) concat(x, y) is just [x, y] when none of x,y are vector types.
> In particular, concat(Vecsmall([1,2]), 3)  is  [Vecsmall([1, 2]), 3]
>
> There are other rules but the above is complex enough already. I don't
> want to add further special cases.
>
> Cheers,
>
>     K.B.
> --
> Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
> Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
> http://www.math.u-bordeaux.fr/~kbelabas/
>