I want to use while in proc but Maple shows an error saying

"Error, (in exa) illegal use of a formal parameter"

When I click on it, as usual it says "There is no help page available for this error". I tried a very simple example of while which you can see it below and it again shows same error. The while works well but when I put it inside of a procedure it makes an error. Note: the following example is just an example, this is not what I'm doing so please don't reply this while proc is not giving anything. My question is how can I use a while in procedure without encountering the above error.

i := 10;
while i > 1 do
if i mod 2 = 0 then i := i/2; else i := i+1; end if;
end do;

Now with proc

exa := proc (i::integer)::integer;
while 1 < i do
if i mod 2 = 0 then i :=i/2; else i := i+1; end if
end do; 
end proc;

exa(10);

"Error, (in exa) illegal use of a formal parameter"

I want to define a proc in Maple which gets an integer n and gives a set of arrays like {1,2,3}^n, meaning {[a[1],...,a[n]]|for all 1<=i<=n a[i] in {1,2,3}}. For a fix n, obviously one can use n-for, for example when n is 2

A:=Array(1..3,1..3):
for a[1] from 1 by 1 to 3 do
 for a[2] from 1 by 1 to 3 do
  A(a[1],a[2]):=[a[1],a[2]];
 end for:
end for:

But when n is not fixed, how can I tell Maple to consider n for?! Also how can ask him to make a n-dimensional array?

Assume we have a map f from a polynomial ring R to another polynomial ring S, I know how to compute kernel (a generator for the kernel ideal) of these maps by Singular, but I want to know can I do it with Maple too? Thanks.

An example;

Consider the homomorphism f:k[x,y]-->k[u,v] sending x to v and y to v^2 then using Singular;

ring r1=0,(x,y),lp;

ring r2=0,(u,v),lp;

ideal i=v,v2;

map f=r1,i;

setring r1;

kernel(r2,f);

_[1]=x2-y

So at above I took k a field of characteristic zero. The kernel is the ideal generated by x^2-y.

What is the easiest way to ask roots of a polynomial on a finite field. For example asking roots of x^2+xy+y on GF(8)? I was thinking to run a two for on members of GF(8) and ask to check it but I couldn't do it using Galois package or maybe I couldn't use that package. Thanks for any help.

Assume we have a sreach with 10 for, for example

answer=0:

for i[1] from 1 by 1 to 5 do

    for i[2] from 1 by 1 to 5 do 

        ...

        if .... then answer=1: print(i[1],...,i[10]); "quitting the search"

        ...

     end do

end do

If I write break at qutting part, it will only exit from one for, one idea is putting if answer=1 break before end do of the rest for, that is why I used the local extra variable "answer" but is this the best idea? Any better idea which contains checking less if is apprecied.