Re: bug in x1=Mod(x+X,X^2+1)^2?

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

On Fri, Dec 29, 2023 at 05:11:47PM +0200, Georgi Guninski wrote:
> Is this a bug?
> 
> ? x1=Mod(x+X,X^2+1)^2
> %11 = Mod(1, X^2 + 1)*x^2 + Mod(2*X, X^2 + 1)*x + Mod(-1, X^2 + 1)
> ? x2=Mod(X+x,x^2+1)^2
> %12 = Mod(2*X*x + (X^2 - 1), x^2 + 1)
> ? norm(x2)
> %13 = X^4 + 2*X^2 + 1
> ? norm(x1)
>   ***   at top-level: norm(x1)
>   ***                 ^--------
>   *** norm: incorrect type in greal/gimag (t_POLMOD).

Yes, x1 is a polynomial and not a POLMOD, due to variable priority.
This explains why %11 and %12 are displayed differently.

Cheers,
Bill