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

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Wed, Mar 29, 2006 at 04:14:08PM +0200, ramare wrote:
> Appele avec : /usr/local/bin/gp -s 100000000 -p 10000000 -emacs
> 
> parisize = 100000000, primelimit = 10000000
> 
> ? Mod(z1,Y^3-1)
> %16 = Mod(z1, Y^3 - 1)
> ? Mod(z11,Y^3-1)
> %17 = 0

I cannot guess what %1 -- %15 look like, but this a consequence
of variable priority: try

parisize = 4000000, primelimit = 500000
? z1;z11;Y
%1 = Y
? Mod(z1,Y^3-1)
%2 = 0
? Mod(z11,Y^3-1)
%3 = 0

parisize = 4000000, primelimit = 500000
? Y;z1;z11
%1 = z11
? Mod(z1,Y^3-1)
%2 = Mod(z1, Y^3 - 1)
? Mod(z11,Y^3-1)
%3 = Mod(z11, Y^3 - 1)

parisize = 4000000, primelimit = 500000
? z1;Y;z11
%1 = z11
? Mod(z1,Y^3-1)
%2 = 0
? Mod(z11,Y^3-1)
%3 = Mod(z11, Y^3 - 1)

In your case the variable priority is z11;Y;z1

So Mod(z1,Y^3-1) live in K(Y)[z1]/(Y^3-1) which is the null space,
but Mod(z11,Y^3-1) live in K(z11)[Y]/(Y^3-1) which is a 
3-dimensional K(z11)-algebra.

Cheers,
Bill.