Re: sqrt(x,n) for non-prime n?

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

On Tue, Nov 21, 2023 at 09:35:53AM +0100, hermann@stamm-wilbrandt.de wrote:
> Modular sqrt does not work with non-prime modulus:
> 
> ? sqrt(Mod(-1,125))
>   ***   at top-level: sqrt(Mod(-1,125))
>   ***                 ^-----------------
>   *** sqrt: not a prime number in sqrt [modulus]: 125.
>   ***   Break loop: type 'break' to go back to GP prompt
> break>

Indeed, but you can do

? issquare(Mod(-1,125),&z)
%3 = 1
? z
%4 = Mod(57,125)

The problem is that when given Mod(a,b) we do not want to have to test b for primality
each time...

Cheers,
Bill.