Re: (Mod(1,2)*x*y)^0

[Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>]

* Bill Allombert [2012-07-17 14:15]:
> ? Mod(1,2)^0
> %1 = Mod(1,2)
> ? (Mod(1,2)*x)^0
> %2 = Mod(1,2)
> ? (Mod(1,2)*x*y)^0
> %3 = 1
> 
> Is it intended ?

Yes :-(

The code to determine "the" base ring for a given polynomial [ RgX_type() ]
was adapted from factor(), and only supports univariate polynomials.

What ^0 does in principle is to return "1" in this base ring. When that
ring can't be determined, as here, we just return the integer 1 and hope
for the best.

The main reason for this behaviour is to avoid checking that the
question even makes sense [ as in Pi*x + Mod(1,2), where it doesn't ].
The code supports all kind of devious constructs involving t_QUAD,
t_COMPLEX with t_INTMOD coefficients, t_PADICs, etc. Right now, whenever
factor doesn't understand what's going on, it just aborts:

(17:06) gp > factor(Mod(1,4)*x+Mod(1,2))
  ***   at top-level: factor(Mod(1,4)*x+Mo
  ***                 ^--------------------
  *** factor: sorry, factor for general polynomials is not yet implemented.


Trying to compute a "common domain" on the spot from an arbitrary collection
of unrelated coefficients is really the wrong approach if one wants sensible
answers in all cases, esp. cases never needed in the PARI library itself.

Cheers,

    K.B.
-- 
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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