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.

I know how to use Maple for an optimization problem contaning continous variables but I couldn't find anything in help of Maple related to use boolean variables in optimization. So assume I want to minimize a function that one of its variables only can take 0 and 1 as its value. Anyone knows how to introduce those to the Maple? For example you can look at this link that Matlab can do many of these kind of optimizations.