Re: [proposal] forvec over cyc

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

Thanks for the pull request. Merged to master. :-)

Cheers,

    K.B.

* Pascal Molin [2022-11-14 14:00]:
> Dear Pari devs,
> 
> I consider the forvec loop one of the top features of GP programming:
> really useful, and painful to write.
> Still:
> - I find myself writing quite a lot forvec(x=vector(#c,i,[0,c[i]-1]), ... )
> - I also need to iterate over the lattice Z^n
> 
> I propose to improve on these two aspects by extending forvec with the
> following additional syntax: if if cyc is a vector of nonnegative integers,
> forvec(x=cyc, ) would iterate on representatives of Z^n/cyc Z^n.
> 
> In particular, if c has positive entries, forvec(x=c, ...) is a shortcut
> for the former forvec(x=vector(#c,i,[0,c[i]-1]), ... )
> And if c=[0,0..0], it would loop on Z^n. A choice has to be made on the
> ordering used, I consider the consider lexicographic ordering graded by
> L^1-norm.
> 
> Specifically, for n = 3, the loop forvec(x=[0,0,0],print(x)) gives
> [0, 0, 0]
> [-1, 0, 0]
> [0, -1, 0]
> [0, 0, -1]
> [0, 0, 1]
> [0, 1, 0]
> [1, 0, 0]
> [-2, 0, 0]
> [-1, -1, 0]
> [-1, 0, -1]
> ...
> (the loop is infinite)
> 
> Finally, if c is a mixed vector of zero and positive values, forvec(x=c, )
> does what I think the most useful : loop on graded-lex elements, with
> torsion components having L1 weight 0 (so one always iterates over torsion
> elements before moving to the next lattice element).
> 
> So that forvec(x=[2,0],print(x)) gives
> [0, 0]
> [1, 0]
> [0, -1]
> [1, -1]
> [0, 1]
> [1, 1]
> [0, -2]
> [1, -2]
> [0, 2]
> [1, 2]
> ...
> 
> I made a branch pascal-forvec-cyc which adds this syntax.
> I used it myself for some time, if this sounds useful for others and
> reasonable for gp syntax I would be happy to have it merged.
> 
> Remark: I did not implement flags, one I could think of is to iterate on
> centerlifts of the quotient.
> 
> Pascal

    K.B.
--
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/
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