Thank you, Preben Alsholm, and I thank also to everybody else. The procedure above works for me, at least until now.  I am really gratfull to everybody, thank you guys.

Ricardo Vieira.

Thank you, Preben Alsholm, and I thank also to everybody else. The procedure above works for me, at least until now.  I am really gratfull to everybody, thank you guys.

Ricardo Vieira.

What I have done to solve this issue is the following:

First I define the object psi := {epsilon^2=1, epsilon^3=epsilon, epsilon^4=1, epsilon^5=epsilon, epsilon^6=1, epsilon^7=epsilon};

And in the expretion F, which I want to simplify, I do

simplify(factor(subs(psi,F)));

The problem with this is that in the evaluation of F, Maple work still with the powers of epsilon and the calculations consume a large time. I want do the maple recognize that, immediately when a product of epsilons appears (that is, when a epsilon^2 appears), then replace it by 1 (in the same way that Maple does the product of I=sqrt(-1).

I was trying to define a symbol epsilon so that epsilon^2=1 but epsilon<>1 (different from 1), but I was not sucessfull with this (Notice that a such number is generally called a 'hyperbolic number')...

I can construct such a objet by a matrix, namely epsilon:=Matrix([[1,0],[0,-1]]), but  I can't do the Maple substitute the powers of epsilon by its symbolic representations again (that is, to it replace the matrices by the symbols epsilon or 1, so that none matrix remais in the equations).

Can anybody helpe-me??

Cordially,

Ricardo Vieira