@marians It appears that you edited the original Question and removed it. Please put it back! It's unacceptable to remove a Question after it's been Answered.

Regarding your latest question, I guess that you want to compute the conjugate using each pair of elements of A and make a new set with the conjugates? Is that correct? And you want to include the cases where i = j (which, of course, just reduces to the set A itself), right?

@acer Ah, I see that it doesn't work for ISOSURFACEs. Thanks for bringing this to my attention.

To correct this, I could search through the 4-d Array for the points where the fourth coordinate is "close to" 0. Then, among those points, search for the extremal values of the third coordinate, which is the z-coordinate. Would that work? The question remains How "close to" 0? What criterion is used by the plot renderer to decide whether to plot a point of an ISOSURFACE? 

@software_c It's common and normal for Maple to re-arrange an expression into a different term order than that with which it was input. Don't use that alone as an indicator that you've encountered a bug.

@Markiyan Hirnyk Do you dispute the cited quotation? Can you present any evidence that it isn't true? Can you cite any source that even casts a shadow of doubt on it? Any hint of doubt on the truth of the cited statement would cause major unrest in the world of cryptography and would definitely make the newpapers and broadcast news. As I said, the statement isn't a proven mathematical fact; it just represents the currently known state of affairs. This is a very, very active area of research.

@Markiyan Hirnyk The facts that I stated are very well-known results of computational number theory---so well known that they are sometimes mentioned in common newspapers. See the Wikipedia article Primality test. Some "algorithms" commonly used for primality testing haven't been proven correct. This includes the one used by Maple's isprime (see ?isprime). It's been proven that there's a theoretically fast (O(ln(n)^12)) primality testing true algorithm; however, I know of no practical implementation of this algorithm.

I invite you to redo my examples with randomly chosen primes.

@dorna01 Since fsolve found a root at

you might as well use something near that as an initial point. I also suggest that you set Digits to 15, but I have no evidence that that'll make any difference in this case. It's just generally a good value for Digits, balancing speed and accuracy.

@vv The plot

plot([Re,Im](DETM2), omega= -1e9..1e9)

leads me to believe that DETM2 is a perfectly reasonable nonconstant function.

There's a syntax error in your construction of the matrix N: An operator is required after the first 20.

@tomleslie Tom, you're right about that syntax error. I assumed that the syntax was correct because plot was happy to plot the real and imaginary parts of DETM2. (I'll have to investigate why that is.) If I correct that syntax error, then fsolve(DETM2 = 0, complex) finds a root in about 10 seconds (in Maple 16 at both Digits = 10 and Digits = 15). That root is

I removed the evalf[4] before doing any of this; however, if I include it, it makes no significant difference in the root that fsolve finds.

@dorna01 

Do you have some reason to believe that a solution exists? Do you have some approximate ranges for the real and imaginary parts? By "numerical techniques", I primarily mean fsolve and DirectSearch combined with some plotting. Unless you're sure that there's a solution and can come up with some ranges, I can't think of anything else in Maple to try.

You can find DirectSearch in the Maple Applications Center. Yes, it runs in Maple 18. It's trivial to install. I need to go to sleep right now. It's very likely that someone else will provide more information very soon.

The error is apparently due to a bug in solve; there's nothing syntactically wrong with your equation. However, there's no hope for obtaining a symbolic solution to such an equation. If there's a solution, only numerical techniques can find it. So, I'm trying with fsolve, and then I'll move to DirectSearch (a third-party add-on package). By plotting, I'm convinced that there's no real solution with magnitude less than 10^8. I will look for complex solutions.

Please post the code and the erroneous use instance.

@kelvin goh But if you include undefined at the end as in the code that I gave, then f(0) <> 0.

Note that "piecewise-continuous" isn't the same as continuous. In case you thought otherwise, there is no need in Maple for a piecewise function to be continuous. Indeed, it can accomodate a step function, as in

piecewise(x < 0, 0, 1)

@sunflower For the third time I'll say that you can't assign to a formal parameter. That means that the line p0:= p produces the error. To correct this, make a local p1 and initialize it to p0. Then never use p0 again.

@sunflower You corrected the first two errors that I pointed out, but not the third: You can't make a direct assignment to a formal parameter. In other words, the line p0:= p is illegal. To correct this, make a local p1 and initialize it to p0. Then never use p0 again.

You'll also need to change diff(f(p0), x) to D(f)(p1).

@sunflower You didn't correctly transcribe what I wrote. The line

det:= LinearAlgebra:-Determinant(A)

needs to be inside the while loop.