@Mac Dude: You are quite right.

But I think that what I meant was just that argument~([complexn1,complexn2,complexn3]) and map(argument,[complexn1,complexn2,complexn3]) are equivalent, a statement I certainly hope is correct :-).

@Torre: Two tiny corrections:
1.) Do you not mean w := evalDG(t*D_x + D_u), rather than w := evalDG(x*D_t + D_u)? Only then does [v,w] give D_x.
2.) The line LD := LieAlgebraData([v,w], alg) does not compute because v and w does not close as a Lie algebra. Only if augmented by D_t, that is, their commutator, will it close.

@MrYouMath: Happy to hear that my suggestion was what you were looking for. And thanks for your kind intentions of giving me a thumbs up point; however, please do not feel obliged to remember that until you gain high enough reputation for doing so :-).

@Kitonum: Specifically, you are absolutely right, of course, but unless I am mistaken, that was not the point of the original poster. I think that what he/she wants is to (gracefully) exit a loop when a certain condition is satisfied. If that condition depends trivially on the loop counter ifself, like the one given in my example, then the code could and should, of course, be rewritten along the lines that you do. But if that is not the case, then I guess there will generally be no such short cut.

@Carl Love: Hopefully a service, here a link to the thread mentioned: Bifurcation in Maple.

@Kitonum: The same reply as to Adri van der Meer.

I only need the Search-command, though, as the elements of the list are assumed non-repetitive.

@Adri van der Meer: I must have been blind. I did look through ListTools prior to posting, but did not locate that command.

Update: Accidentally (still sleeping, apparently), I have just applied the command to a Vector, rather than a list. Surprisingly, it works there as well.

@sand15: Happy to hear that you have reached the same conclusion.

@Joe Riel: I was actually thinking the same concerning deletion of spam. Having just discovered it, there is indeed the option 'Delete as Spam' on the 'More'-button for the top-post of a thread.

@Bryon: It's reassuring to know.

@acer: Then it makes more sense to me. Thanks.

@rlopez: That is indeed simpler; as simple as it can get, I suppose.

@Markiyan Hirnyk: I had a hunch that a simpler version of mine surely existed :-).

From the limits

limit(normSquare,x = +infinity) assuming b < 0;
limit(normSquare,x = -infinity) assuming b < 0;
∞
0

it follows that b cannot be negative. From the limits (for the remaining non-negative b)

limit(normSquare,x = +infinity) assuming b >= 0;
limit(normSquare,x = -infinity) assuming b >= 0;
0

it follows that the numerator inside signum (sign function for real and complex expressions) must vanish if both limits are possibly to vanish. Being equal to a^2 + (b - 1)^2, i.e., a sum of squares, this will happen only for (a,b) = (0,1), corresponding to k = I.

@sand15: Absolutely no need to apologize. By the way: If you realize that you have made a mistake shortly after submitting a post, you can delete it altogether by clicking the 'More'-button to the very right below your post, and then choose 'Delete'; if you want to edit a post, you can do it under the same button. In fact, it seems that you can delete the post even after someone have responded to it (update: that may, however, only be possible for members with sufficiently high reputation scores, I have subsequently learned); that, however, would perhaps be a bad idea as it would disrupt the thread.

Anyway, I am unable to verify your claim that "boundedness only occur for pure imaginary k", if you by that means any purely imaginary k. Rather, it seems to me that only k = I works, although I have not proved that yet. For instance, for k = 1.001*I, say, the normSquare (as defined above) has the following (interesting) graph: