Re: equality of t_INTMODs

[Denis Simon <denis.simon@unicaen.fr>]

Hi all,

if I understand well the discussion, the relation == is not transitive, but === is.
Example : 
Mod(14,20) == Mod(39,55) == Mod(4,20)
but not Mod(14,20) and Mod(4,20) 

Denis SIMON.

----- Mail original -----
> De: "Karim Belabas" <Karim.Belabas@math.u-bordeaux.fr>
> À: "Max Alekseyev" <maxale@gmail.com>
> Cc: "Pari Users" <pari-users@pari.math.u-bordeaux.fr>
> Envoyé: Vendredi 24 Janvier 2025 17:23:14
> Objet: Re: equality of t_INTMODs

> 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/