Re: equality of t_INTMODs

Karim Belabas <[email protected]> Fri, 24 Jan 2025 18:11:36 +0100

Newsgroups	gmane.comp.mathematics.pari.user
Message-ID	<[email protected]>

* Max Alekseyev [2025-01-24 17:56]:
> Hi Karim,
> 
> On "===" vs "==", what are other notable cases when the two give different
> results?

There are many:

  ? 1. == 0E38 \\ at default precision
  %1 = 1

  ? [] == 0
  %2 = 1
 
  ? 1 == [1,0,0]~
  %3 = 1

  ? Mod(1,2) == 1
  %4 = 1

etc.

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

Mostly yes. They rely on cmp(), which is a universal comparison function.
Mathematically meaningless but transitive, and it guarantees
  cmp(x,y) == 0 if and only if x === y

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-prÃ©sident en charge du NumÃ©rique
Institut de MathÃ©matiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/