@isifesai The Interpolation package is new to Maple 2018. With some small adjustment of Mariusz's code, you could replace it with CurveFitting:-ArrayInterpolation.

@Carl Love Using the process that I described, this is what I got for w[2](y,z) and w[3](y,z):

w[2](y,z);

-y*cos(z)*sin(z)/exp(y)

w[3](y,z);

(y^2*cos(z)^2*sin(z)*exp(y)+4*cos(z)^2*sin(z)*y*exp(y)-cos(z)^2*sin(z)*exp(y)-2*y*exp(y)*sin(z)+cos(z)^2*sin(z)+exp(y)*sin(z)-sin(z))/(2*(exp(y))^2)

@tomleslie Yes, good, vote up.

@dharr Oops, my thinking about this was backwards. When there are parameters the generic case is in general the defective case, and having a complete basis of eigenvectors is the exceptional case. Just think about A:= < 0, x; 0, 0 > for a moment. It's nondefective iff x = 0. If you do LinearAlgebra:-Eigenvectors(A) (without any other options or adjusting Normalizer), the returned matrix of "eigenvectors" contains a column of zeros. This column is not an eigenvector (the zero vector is never an eigenvector).

Nonetheless, my fundamental point that the number of eigenvectors depends on the parameters and requires case-wise analysis remains, and my title "Parameters may make it defective" still applies. I edited the Answer accordingly.

@tomleslie The same comment that I just made to Kitonum applies here as well. Is there something wrong with using Logic:-TruthTable(..., form= MOD2) for this? To me, it seems ideal for this plotting application.

@Kitonum While it's true that it's not, strictly speaking, necessary to use Logic for this, is there some good reason to not use it? The DataFrame output of Logic:-TruthTable is far more convenient to work with than your ad hoc sequences of true and false.

@Earl Thanks. The example, worksheet, and MathWorld link are sufficient.

@jthress1 Eigenvectors are, by defintion, never the zero vector. Eigenvalues may be 0, but not eigenvectors. If we were to allow 0 as an eigenvector, then any scalar would be an eigenvalue corresponding to it.

Surely the minimal surface exists; the question is whether a formula for it is known or can be found. Can you give the catenoid's formula or a reference for it? For simplicity, just assume that one circle is the unit circle.

@Seb1123 We learn in high-school algebra that one simplifies expressions whereas one solves equations or inequalities. Maple's simplify dd the only thing that's consistent with that model: It maps itself over the two component expressions that make up your equation---the left and right sides.

(In Maple-speak, an equation (or nearly any other fragment of code) is sometimes called an expression. But that's not the way that those words are used in high-school algebra.)

@Earl The worksheet "OnionExtended" in your most-recent Reply is identical to the one from your earlier Reply.

Also, when I say "embed the executed worksheet inline in your post", I mean that the entire worksheet---all input, output, and plots---should be directly visible in the post, without needing to be downloaded.

@digerdiga When you use f2(m), it attempts to do a numeric integration with a symbolic parameter m. That's usually a bad idea, although there may be some rare cases where it's useful. The fact that you've specified numeric values for m with m= 3..10 is irrelevant because the f2(m) is evaluated before being passed to plot. This is the default order of evaluation (for almost all commands---not just plot): Evaluate the arguments first, then pass them. There are numerous ways to get around that, and you've shown one of them: procedure-form input: plot(f2, 3..10).

@Earl I attempted to run your worksheet "OnionExtended" in Maple 2018. I just used menu Edit -> Execute -> Worksheet (same thing as Ctrl+Shift+Enter from the keyboard or !!! from the toolbar). Every Onion command returns an error. I'm almost certain that this is because it is trying to use stuff from your personal library that I don't have. In particular, it is trying to use Plot3Daxes. (That's just an example; there are probably other items from your library that it's trying  to access.)

Would you please do something about that? And when you repost, please embed the executed (with the plots) worksheet inline in your post, assuming that MaplePrimes will do it (there are some worksheets that are complicated display-wise that it balks at).

Best regards,
Carl Love (posting as a MaplePrimes moderator)

@tzeng There is no difference between between assume(phi, real) and assume(phi::real). In your code you used simply phi::real rather than assume(phi::real).

I prefer the A::B syntax. It's used in many places in Maple, and it makes it clear to your readers that B is either a property (such as real) or a type (as in L::list(name)).

The A::B syntax, standing alone as in your usage phi::real, is inert. It doesn't do anything until you make it part of another command, such as an assume command.

@tomleslie I find the slideshow feature slightly useful when I'm actually giving a slideshow, with a projector and a live audience. But it does involve a great deal of preliminary work (hours) to get the sections set up just right.