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

On 2025-05-27 00:40, Bill Allombert wrote:
>> 
>> 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.
> 
Thank you, so the rem part is what I asked for.
Interesting, "i" is free variable and not sqrt(-1) which is "I" in GP.

Now that type(b) is t_POL, Mod(a,b) works as well.
What is the meaning of "-5" in Mod(a,b) result?

? a=1+4*i;b=3+2*i;
? Mod(a,b)
Mod(-5, 2*i + 3)
?

Regards,

Hermann.