Re: PARI/GP vecsort/versearch and Mod()

[hermann@stamm-wilbrandt.de]

On 2025-11-15 17:01, Bill Allombert wrote:
> On Sat, Nov 15, 2025 at 03:48:05PM +0100, hermann@stamm-wilbrandt.de 
> wrote:
> > I wanted to check four 2x2 matrixes with entries in ℤ/2ℤ to be closed 
> > under
> > matrix addition and multiplication.
> >
> > Because of missing order relation for Mod() using vecsort/vecsearch 
> > directly
> > was no option.
>
> You have three options:
> - Use Set and setsearch
> - use Map and mapisdefined
> - use vecsort/vecsearch but apply lift to the vectors/ elements to
> remove the Mod.
>
> Cheers,
> Bill.
Thanks, your 3rd option is what I described.

How to make this work and get rid of 1st } and 2nd { ?
So all in one outer pair of braces?

$ gp -q < F4.new.gp
{0,1,a,b} is closed under matrix +
$
$ cat F4.new.gp
assert(b,s="")={if(!(b),error(Str(s)))};
{
  F4 = [[Mod(0,2),Mod(0,2);  \\ 0
        Mod(0,2),Mod(0,2)],
       [Mod(1,2),Mod(0,2);   \\ 1
        Mod(0,2),Mod(1,2)],
       [Mod(0,2),Mod(1,2);   \\ a
        Mod(1,2),Mod(1,2)],
       [Mod(1,2),Mod(1,2);   \\ b
        Mod(1,2),Mod(0,2)]];

  slF4 = vecsort(lift(F4));
}
  inF4(M)={vecsearch(slF4,lift(M))};
{
  foreach(F4,a,
    foreach(F4,b,
      assert(inF4(a+b),"add not closed")));
  print("{0,1,a,b} is closed under matrix +");
}
$


Regards,

Hermann.