Re: equality of t_INTMODs

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 <
[email protected]> 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 <
> > [email protected]> 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/
>