Re: Bug in Mod (2.0.15)

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

> On Wed, Mar 01, 2000 at 06:51:04PM +0100, Karim BELABAS wrote:
> > >     ? z=Mod(x,x^2+y^2)
> > >     %1 = Mod(x, x^2 + y^2)
> > >     ? u=Mod(z,x^2+y^2+t^2)
> > >     %2 = 0
> > 
> > It's a (debatable...) feature : modular objects (POLMOD/INTMOD)
> > of different modulus are adjusted to a common modulus first, here
> > gcd(x^2 + y^2, x^2 + y^2 + t^2) = 1, and all objects mod 1 are equal to 0...
> 
> Eh?
> 
> ? Mod(0,1)
> %1 = Mod(0, 1)
> 
> They may be equal to 0, but they are definitely not 0.

Just the same here. An algebraic number (t_POLMOD) which is equal to 0 is
printed as zero.

(13:01) gp > z = Mod(x,x^2+y^2)
%1 = Mod(x, x^2 + y^2)
(13:01) gp > u = Mod(z,x^2+y^2+t^2)
%2 = 0
(13:01) gp > %2.mod
%3 = x^2 + (y^2 + t^2)
(13:01) gp > %2.pol
%4 = Mod(0, 1)  \\ 1 = gcd(x^2+y^2, x^2+y^2+t^2)

BUT:
(13:01) gp > u.pol
%5 = Mod(x, x^2 + y^2)

the "problem" (due to the phenomenom alluded to in my previous mail) actually
occurs while simplifying the expression (just before printing, but after the
assignment u = ...)

(13:01) gp > \y
   simplify = 0 (off)
(13:01) gp > u = Mod(z,x^2+y^2+t^2)
%6 = Mod(Mod(x, x^2 + y^2), x^2 + (y^2 + t^2))

which is an incorrect object... Mod() currently only checks its second
argument, leaving the user responsible for the other one. This follows the
"PARI philosophy" [ try to make sense of most input, and let the user shoot
himself in the foot if she wishes ]. Again, this should probably be revised
(generic functions are far too permissive in my opinion).

   Karim.
__
Karim Belabas                    email: Karim.Belabas@math.u-psud.fr
Dep. de Mathematiques, Bat. 425
Universite Paris-Sud             Tel: (00 33) 1 69 15 57 48
F-91405 Orsay (France)           Fax: (00 33) 1 69 15 60 19
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