Re: equality of t

Hi Karim,

On "===" vs "==", what are other notable cases when the two give different results?

Do I understand correctly, that internally functions in PARI/GP, such as setsearch(), rely on "===" rather than "=="?

As for "==" for t_INTMODs, it looks like it's better understood as non-disjointness of the corresponding residue classes. What is confusing though is that such non-disjointness is denoted by equality.

Maybe, it's affected by my (default) view of t_INTMOD as a residue class, but in reality it's a more relaxed thing.

Regards,

Max

On Fri, Jan 24, 2025 at 11:23 AM Karim Belabas <Karim.Belabas@math.u-bordeaux.fr> wrote:

Hi Max,

we recommend using

a === b (is identical to)

rather than the much more liberal and more costly

a == b (is equal to; in the sense of "there is a natural map sending a
to the domain of b or sending b to the domain of a, such that the
comparison makes sense and equality holds")

Cheers,

K.B.

* Max Alekseyev [2025-01-24 17:11]:
> Hi Karim,
>
> After the fix we have
>
> ? Mod(14,20) == Mod(39,55)
> %1 = 1
>
> I understand why, but nevertheless it looks very confusing.
>
> Regards,
> Max
>
>
> On Fri, Jan 24, 2025 at 10:58 AM Karim Belabas <
> Karim.Belabas@math.u-bordeaux.fr> wrote:
>
> > Hi Max,
> >
> > * Max Alekseyev [2025-01-24 16:12]:
> > > In view of a recently discovered issue in Sage (
> > > https://github.com/sagemath/sage/issues/39372), I'd like to check how
> > the
> > > following two (in)equalities co-exist in PARI/GP. Do they violate any
> > > design conventions and/or represent a notable exception to those?
> > >
> > > ? Mod(14,20) == Mod(39,55)
> > > %1 = 0
> > > ? Mod(14,20) - Mod(39,55) == 0
> > > %2 = 1
> >
> > They do violate the design convention (x == y iff x - y == 0;
> > use the === operator for proper equality without implicit coercion).
> >
> > t_POLMOD had the same issue. Both issues are now fixed in 'master'.
> >
> > 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/
> >

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/