Re: Mod(z11,Y^3-1) =??? 0

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

* ramare [2006-03-29 17:01]:
[...]
> ? Mod(z1,Y^3-1)
> %16 = Mod(z1, Y^3 - 1)
> ? Mod(z11,Y^3-1)
> %17 = 0

Provided the variables were introduced in the order (z11, Y, z1), this
is the expected behaviour, see section 2.5.4 ("Variable priorities,
multivariate objects").

Short answer: Q(Y) / (Y^3-1) is the zero ring, hence so is Q(Y)[z11] / (Y^3-1).

This is a well known design bug in PARI multivariate polynomials. There is
no (sensible) way to fix (and more importantly change, or override) a
variable ordering, except by getting it right from the start.

Cheers,

    K.B.
-- 
Karim Belabas                  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-bordeaux.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]