Re: How to determine Mod(a,b) with t_COMPLEX b?

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

On Tue, May 27, 2025 at 12:01:44AM +0200, hermann@stamm-wilbrandt.de wrote:
> $ gp -q
> ? a=1+4*I;b=3+2*I;
> ? a/b
> 11/13 + 10/13*I
> ? Mod(a,b)
>   ***   at top-level: Mod(a,b)
>   ***                 ^--------
>   *** Mod: forbidden division t_COMPLEX % t_COMPLEX.
>   ***   Break loop: type 'break' to go back to GP prompt
> break>
> 
> 
> The minimal residue of 1+4*I modulo 3+2*I is the yellow point -I in the
> example:
> https://en.wikipedia.org/wiki/Gaussian_integer#Describing_residue_classes
> 
> How can minimal residue of an input gaussian integer modulo a gaussian
> integer be computed in PARI/GP?

nf=nfinit(i^2+1)
a=1+4*i;b=3+2*i;
nfeltdivrem(nf,a,b)
%4 = [[1,1]~,[0,-1]~]

Cheers,
Bill.