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

[hermann@stamm-wilbrandt.de]

On 2025-05-27 18:27, hermann@stamm-wilbrandt.de wrote:
> >
> I found the reason for no difference — real(b) and imag(b) were 
> relative prime.
> If not relative prime, there are differences:
>
> ? b*=2
> 6 + 4*I
> ? S=Set([a - round(a/b)*b |
> r<-[-real(b)..real(b)];i<-[-imag(b)..imag(b)];a<-[r+i*I]]);
> ? myS=Set([a - myround(a/b)*b |
> r<-[-real(b)..real(b)];i<-[-imag(b)..imag(b)];a<-[r+i*I]]);
> ? #S==norml2(b)&&#myS==norml2(b)
> 1
> ? setminus(S,myS)
> [-3 - 2*I, -1 - 5*I, 2 - 3*I]
> ? setminus(myS,S)
> [-2 + 3*I, 1 + 5*I, 3 + 2*I]
> ?
Last, but not least, a picture:

? b
6 + 4*I
? imi=vecmin([imag(s)|s<-S]);
? ima=vecmax([imag(s)|s<-S]);
? rmi=vecmin([real(s)|s<-S]);
? rma=vecmax([real(s)|s<-S]);
? M=matrix(ima-imi+1,rma-rmi+1);
? foreach(S,s,M[imag(s)-imi+1,real(s)-rmi+1]=1)
? foreach(M~,m,foreach(m,e,print1(if(e,"x"," ")));print())
   x
   xx
  xxxxx
 xxxxxxx
 xxxxxxxx
xxxxxxxxx
xxxxxxxx
 xxxxxx
   xxxx
    xx
?


Regards,

Hermann.