Say I define the following variables.

These are all nineth roots of unity. An equivalent definition would be:

In fact, the following code shows that aa[i] /a[i] =1 for all i, so one would concluse aa[i]=a[i]:

for i to 9 do 
simplify(a[i]/aa[i])
end do

But when I try to check via "Equal":

I get as output

                              true
                             false
                             false
                             false
                             false
                             false
                              true
                             false
                             false
The problem goes even further since one representation is accepted as a solution of a linear equation system while the other is not.

Another curiosity:

gives just the same expression, whereas simplifying the same expression to the third power gives 0.

Hi,

say I have defined some (very simple, acting on a finite set M) functions f,g,h. I want to evaluate certain permutations, so I want to make a for loop that goes through possible combinations of functions in my array A=Array([f,g,h]). (In reality my array is a little larger.) No I don't understand how I can use the elements of this array as actual functions. Even if f is defined and I can evaluate, say, f(m), I cannot use A(1)(m) to evaluate m. The output is just "f(m)". How can I make maple recognize that we are having a function here?

Thanks it advance.