@Preben Alsholm 

A great substitution; I didn't know that IntegrationTools:-Change could make use of assumptions. Vote up. In some versions of Maple (notably Maple 16), an expand may be required before the eval to force the y outside the integral to cancel with the y in the denominator of the integrand.

If Gamma is entered as the exact value 1/5 rather than 0.2, you can use value on the integral and prove that it is exactly 1.

@ecterrab 

If you are using 1D input, there is a preliminary step needed before you can use Edgardo's Answer. Highlight the expression, right click, and Convert To -> 2D Math Input. Then follow Edgardo's instructions.

@hazif firas 

Sorry, I can't solve your problem. I got past the "initial Newton..." error, but then I get a division by zero.

I just want to point out that Runge Kutta Fehlberg 4 5 (rkf45) is a method for IVPs, not BVPs. There is no way to tell Maple to solve a BVP with rkf45.

I haven't looked at your worksheet yet (I will). But I want to point out that undefined and Float(undefined) are not errors; they are mathematically valid answers. For example limit(1/x, x= 0) is undefined.

@sercan 

Can you supply ranges for the constants and variables? For example, are any of them guaranteed to be positive? Are there also relations such as w > c that hold? Maple can often prove an inequality when given some assumptions on the variables.

By "better", I assume that you mean ProfitB >= ProfitC for all values of the variables and and constants. Is that right? Then there's really no distinction between variables and constants.

[I edited your Question due to excessive whitespace.]

I doubt that there's any simplification for that. Just looking at n=2, I see no simplification. Are you sure that you want a summation rather than a product? If you change Sigma to PI (Maple command product) then there's a simplification.

Is the issue that you want to prove that the functions are identical?

How about posting your Maple code with the functions?

@Kitonum 

Change 3 to length(j).

@nm 

There is nothing wrong with having text or any other data structure in a matrix. Indeed, certain commands in Maple require an Array, Matrix, or Vector of plots. I understand your point about "lists of lists," but note that a Maple Matrix is different from a Maple list of lists.

There is nothing wrong with having keys in a set.

@mzaman 

My guess that using the timelimit wouldn't be worthwhile was correct. But I include the technique here to show how to use the command. In the worksheet below, I call it with the minimal amount of time, .01 seconds. I tried it at 5 seconds, but the program ran for 40 minutes without completing any factorizations.

I also improved the code for selecting the kp2 closest to 56 bits. In the run below, you can see that p is 511 bits and q is 512 bits.

Download WuSun.mw

@gdoug 

What version of Maple are you using? The above works for me, even with a single vector, in Maple 16 through 2015.

Also, did you cut and paste the code exactly as I had it? Or did you retype it? If you retyped it, please post the retyped version here.

@Yiannis Galidakis 

Those are wonderful animations. Could you post the Maple code to generate them?

And your Reply above would make an excellent Post. Please consider Posting it.

What makes you think that the precision is currently set at 100 digits? The default is 10. To control the number of digits, set the Digits environment variable. For example,

Digits:= 15:

However, I doubt that reducing the number of digits will do much to speedup your problem, even if your precision is currently 100.

How about posting your code?

@J4James 

What "issue" do you mean? And what is the significance of the plot that you posted? It has three curves. The sum from 10001 to infinity (the part that I truncated) is much too small to make any difference in the plot!