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

On 2025-11-15 17:01, Bill Allombert wrote:
> On Sat, Nov 15, 2025 at 03:48:05PM +0100, [email protected] 
> 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.