@Markiyan Hirnyk It is not a trick because I know a priori that h3 is real. It is a mathematical certainty. So I keep applying simplifiers until it looks real.

@J4James

Since you define DP3 as a procedure with parameters Q and tau, why are you using subs to supply the value of tau ???

@Markiyan Hirnyk 

If you integrate and plot that simplified expression, you will get exactly the same plot that you got by your technique.

You have not provided any mathematical reasoning as to how h3 could be non-real.

@Markiyan Hirnyk 

Cosine is a real-valued function for real arguments. h3 is a sum of cosine terms times something plus something. How could it possibly not be real, given that the parameters are real?

@ANANDMUNAGALA 

You may be looking for the command DEtools[DEplot].

@lonelyoak 

I have a solution for your problem, but I don't know if you want me to post it. Let me know.

The [] do indeed indicate that there are no solutions for those ranges. I do not understand the 0, but it is not a valid solution. It might have something to do with a default value for piecewise. Note that epsilon=0 is invalid anyway.

Please post your actual code and the actual results from solve.

The square brackets may be due to a recently discovered bug involving piecewise solutions given by solve. The 0 does not mean all parameters equalling 0 because solutions should be listed individually for each parameter. However, I need to see it to interpret the 0.

Your code is missing procedure definitions for Bt and BzProc.

@Muhammad Ali Now that the algorithm is settled, we can overload the ordinary minus operator so that "list minus" works seamlessly with the same syntax as regular set minus. In Maple 17 or 18:

If you have Maple earlier than 17, it can still be done. Let me know.

Download list_minus.mw

@karolis It is a bug in the MaplePrimes software. If you try uploading the file again, it might work.

Please show your code.

@Muhammad Ali Whether an Array or a table is faster depends on the operation. Let n be the size of the structure: table, Array, set, list. Searching the structure for a particular item takes

• table: O(1)  (when you're searching the indices, not the entries)
• Array: O(n)
• list: O(n)
• set: O(log(n))  (because sets are stored sorted)

Constructing the structure takes

• table: O(n) ??? (Not sure about this one; might be O(n*log(log(n))).)
• Array: O(n)
• list: O(n)
• set: O(n*log(n))

@Alejandro Jakubi Yes, that worked. Thanks.

@mehran1520 You need to download the module package DirectSearch from the Maple Applications Center.

Can you give ranges or sample values for the parameters C1, C2, M, Q, lambda, and tau? Obviously you have some if you intended to plot it.

The most likely scenario is that numeric evaluation of the expression over the region of interest yields imaginary parts very close to zero. These imaginary parts are due to round-off error in the floating-point evaluation. They would be zero in exact arithmetic. These can be safely removed by applying Re to the expression. But you must first check that the imaginary parts are close to zero.