@Carl Love Axel's method of changing the numeric integration method is much faster than mine.

@PunkRediska Your expressions are too long for me to cut-and-paste. Would you please upload a worksheet with the definitions of the four variables Vx, Vy, xxx, yyy? The worksheet doesn't need to have anything else, if that helps.

A quick glance indicates to me that your functions have an extreme number of points of non-differentiability.

To get any help, you'll need to post the code for your preliminary steps such as Vx, Vy, xxx, and yyy.

@Arka The expression can't be factored other than factoring out the constant 16. You can easily prove that (pp1^2+pp2^2+pp3^2) is not a factor by evaluating a at integer values for all the variables and then checking whether the result is divisible by (pp1^2+pp2^2+pp3^2):

A:= eval(a, [Q1=3, Q2=5, Q3=7, Q4= 11, pp1= 13, pp2= 17, pp3= 19]);
                          53328924928
P:= eval(pp1^2+pp2^2+pp3^2, [pp1= 13, pp2= 17, pp3= 19]);
                              819
A/P;
                          53328924928
                          -----------
                              819    

@Arka Then the expression is not factorable as entered. Since you posted your expression as an image rather than as plaintext, I cannot work with it.

@Markiyan Hirnyk What is your point? The options numpoints and gridrefine are not mutally exclusive; options numpoints and grid are. Option numpoints determines the initial grid.

@Carl Love Continuing from above, arbitrarily select omega = 12, so omega^(-1) = 17. Then the matrix DFT is

DFT:= Matrix(4,4, (i,j)-> 12^(i*j) mod 29);

and the inverse transform matrix is

IDFT:= Matrix(4,4, (i,j)-> 17^(i*j) mod 29);

You can verify that their product is 4I by

DFT.IDFT mod 29;

@abbeykabir Sorry, I can't think of any reasonable way to plot a parametric curve over the complex numbers. If it were possible to express it as y = f(x), then there are some possibilities. But that is not possible for this x and y.

@sunit Ah, I see. Was the restart in the .m files? Then that's the problem. The restart only works at the top level, not in a file, and it should be placed in its own execution group.

@sunit So, essentially, you were making the assumptions twice.

@Joe Riel Thanks, Joe. I corrected the Answer above.

@Preben Alsholm Preben, Your eval trick does not work for me. I still have kernel death. I also have kernel death if I replace add with seq or mul, or if I make the equivalent construction with $. Indeed, if I make the line the simple 

C[i]*d[i] + C[i];

then I still have kernel death.

@Preben Alsholm You asked:

By T(N^2(z)) do you mean T(N(z)^2) or do you mean T(N(z))^2?

Neither. By T(N^2(z)) the OP means T((N@@2)(z)), and by (T(z))^2 the OP means T(z)^2.

@Alejandro Jakubi He is saying that the procedure BlahMethod, the export of the module, is not (explicitly) executed. Nonetheless, that is the procedure that contains the statement that causes the crash.

@abbeykabir Yes, I got the same plot.