Re: Oddities modulo multivariate polynomials

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

On Thu, 9 Oct 2003, Dirk Laurie wrote:
> Jeroen Demeyer skryf:
>> ? Y                   /* Make sure Y is defined first */
>> %1 = Y
>> ? (Y^2) % (X^3 - Y^2)
>> %2 = X^3
>> ? (X^3) % (X^2 + 1)
>> %3 = -X
>> ? ((Y^2) % (X^3 - Y^2)) % (X^2 + 1)
>> %4 = 0
>>
>> How come the outputs of the two last statements are different?  Is this
>> a bug or am I doing something wrong?  Any help would be appreciated.
>
> A very pleasant problem in detection!  Let's get some more data.
> Start from scratch each time in a new Pari-GP session.
[...]
> The hypothesis so far stands up.  To explain your original
> result: I guess that once the decision has been made, it
> remains in effect for the whole expression.  So that in
> an expression like the one giving your %4, the independent
> variable is Y, since it was defined first.  You can't
> have Y as independent in one subexpression and X in the other.
> Whereas in %3 there is no ambiguity.

There is a section 2.6.2 to explain this in the users manual, unfortunately
in the _unstable_ version. [ Sorry, I do not backport documentation
changes... ]

I would recommand trying out the unstable branch (2.2.*) nowadays. It is very
close to beta status, and definitely contains far fewer documented bugs than
the stable one.

Cheers,

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]