Re: vecsort() and sign()

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

* Max Alekseyev [2018-02-20 01:40]:
> In the extended help for 'vecsort' I read:
> "a comparison function (*t_CLOSURE*), with two arguments $x$ and $y$, and
> returning an integer which is < 0, > 0 or = 0 if x < y, x > y or x=y
> respectively. The *sign* function is very useful in this context:"
> which is followed by examples like
> ? vecsort(v, (x,y)->sign(abs(x)-abs(y)))  \\ *sort by increasing absolute
> value*
> However, I do not see how sign() is useful here. From the definition of
> vecsort(), it follows that
> ? vecsort(v, (x,y)->abs(x)-abs(y))
> would work equally well.
> So I wonder why enveloping the cmpf function with sign() is "very useful"
> and why?

This is historical: a long time ago, the comparison function was
required to return 1, 0 or -1. The sign function is now useless for
vecsort, I have updated the documentation.

> Also, the build-in help for vecsort() says:
> "If cmpf is an integer, sort according to the value of the k-th component
> of each entry."
> First, it's not clear what is k here. Perhaps, it should say "if cmpf
> equals an integer *k*" or something like that.

Done ! In fact, this is a rather useless construct since it's trivial to
emulate it with (x,y)->x[k]-y[k]. A much more useful one is k = [1,3,2]
(sort by 1st entry, then 3rd, then 2nd: this one is more painful to emulate
with a closure...).

> Second, my first thought was that I can use vecsort() to sort a vector of t_
> INTMOD based on the value of moduli. Indeed, the modulus of t_INTMOD x
> equals component(x,1), so supposedly
> ? vecsort([Mod(2,3),Mod(1,2)],1)
> should work, but it does not.

Indeed, "component" is a bad choice of words given the existence of
component(). The function is specific to t_VEC (and t_COL) entries.

You can use

  vecsort(v, (x,y)->component(x,1)-component(y,1))
or
  vecsort(v, (x,y)->x.mod-y.mod)

explicitly, of course. I would myself use the second one, even if
component(x,1) was implied by the "k = 1" construct.

> So, I wonder if vecsort() can be easily extended to sort objects on any
> types based on the value of component(x,k) (for a given cmpf=k) or it's
> very specific to vectors and cannot be extended to other types.

It's easy to do, I'm not sure how useful it would be. I would find it
confusing given that the meaning of "component(x)" depends very much on
the type of x: an explicit comparison function seems best when a
non-trivial component is implied.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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