I've provided an example to show the difference "Simplify" does.
First, if I use simplify I get the correct answer in the end of the procedure but I need a lot of memory and time, and if I don't use simplify I get a wrong answer, so it is mandatory to simplify in order to obtain a correct result.
Next, simplify is used in a for loop, so I asked maple to show me the result (with and without simplify) on each iteration to understand the difference that "simplify" makes and the type of simplification we need.
On the left-hand side of the equation above, we have the expression returned by maple without any simplification, while the right-hand side is the expression after using Simplify and which we need to obtain the correct result.
Same for these examples below:
Do you know any alternative method to simplify that would yield results much faster ?