@hojat Lambda still has a 1[1] and a 2[1].

@hojat Please confirm that you are minimizing a function of 12 variables (from indets(Lambda,name) ). If so this will be an extremely difficult problem and I'm guessing it generates some complex numbers because it doesn't know enough about these values. What are the approximate values of these variables? For nonlinear problems, an initialpoint is almost certainly needed.

@ianmccr This recasting into alternate forms happens in several situations, including just printing the code of a procedure with a semicolon. Since these are often less readable, I find this frustrating but don't know of a workaround.

@sursumCorda I see there that the symmetric NAG routine is recommended over the general one because it is "more accurate", so a NAG general routine is probably not useful here (can't increase digits then) though the specialized ones may be. Maple probably has a special routine for exp (I didn't check), which is why @Axel Vogt's method works.

Detecting the non-diagonalizable case will always be difficult if Jordan forms are used, because that is a difficult computation. Eigenvectors returns a "zero eigenvector" in that case but how close to zero does it have to be to be detected? [Edit: I see Eigenvectors can just output the true eigenvectors, so has some detection method for this.] These situations, including when two numerical eigenvalues are the same, rely on some careful assessments and are tricky in general - maybe the linalg method that worked well in this case would not work so well in other cases.

However, the fact that it is so bad in quite a few cases means it needs some improvement for sure.

@tomleslie Yes, it is interesting how often this question is asked. Perhaps it should be in huge letters on the help pages for plot and plot3d.

@sursumCorda I had a closer look into how the algorithm works, and my analysis below suggests in the numerical case, close eigenvalues that should be detected as degenerate are not in LinearAlgebra:-MatrixFunction, but are in linalg:-matfunc. I have submitted an SCR.

For going beyond, the normal case is well-behaved and can be done just by applying the function to the eigenvalues in a unitary decomposition (Horn and Johnson, Theorem 6.2.37). So for numerical matrices with shape=symmetric or shape=hermitian (or the skew versions), that would be a separate case worth doing.

Download MatrixFunctionAlgorithm.mw

@ishan_ae I'm guessing that you didn't add two unevaluation quotes around the add: '' add '' (these are two ' not one "). This is an endless problem in Maple. One way to solve not knowing how many is just to have one in the definition, and then add a "numeric" option, which effectively tells animate not to bother unless a number is provided. The output of the fourier_f definition is now ugly.

fourier_analysis_numeric.mw

Or you can use Sum, but then you need value:

fourier_analysis_Sum.mw

@ishan_ae

I changed to assume n is a positive integer, then the sin(n*Pi) and cos(n*Pi) can be simplified. assume(N>0) has no effect since the N within the fourier_f is not the same as the one outside.

The delayed evaluation quotes around 'add' are because at the time the fourier_f definition is evaluated, the value of N is not known. This prevents add from generating an error because N does not yet have a value. In the animated one, I have needed to do this twice.

display is in the plots package so needs to be plots:-display (or use with(plots): at the start of the worksheet).

If you use sum instead of add, it tries to work out the general formula every time sum in encountered, which slows it down significantly.

Here it is working.

Download fourier_analysis.mw

Not clear if this is OK - you can remove input from the worksheet using view->show/hide contents and then export to .pdf (or print to .pdf with a .pdf printer driver)

@sursumCorda Finally got a version with topological sort to work, added to the above - about twice as fast.

[Edit - I removed a redundant line of code and now can't reproduce the faster timing - it's about the same.]

Have never used these and they might not be what you want, but there is a Grading package, and Maple TA. The help page ?MapleTAIntegration has a number of useful links.

This works for me so presumably something about your installation is different. I suggest you contact technical support

compile_ex.mw

@sredh01 Your main problem is the absence of the RandomMatrix(n,n,generator=-5..5): Here's a version that generates a given number of matrices.

GivenDet2.mw

@ijuptilk I interpreted your question "Hi, please can someone help on how non-dimensionalize PDEs. I have tried the following, but is not working" as meaning "I know how to non-dimensionalize, and was in the process of non-dimensionalizing when Maple gave an error, so could someone please solve the Maple error". So I made the various substutions exactly as you had them. You presumably actually know the dimensions of various quantities, and I wouldn't normally attempt a non-dimensionalization without that information.

More generous MaplePrimer @sand15 = @mmcdara interpreted your question as requesting a complete solution to non-dimensionalize your equation. But they are slowed down in this by having to deduce things, like the f[1] and f[2] interpretation, which you have only now provided, and now we see that K[1] and K[3] appear more often than they did in the original equation. So are you OK with a solution without f[1] and f[2]? Your response is not very clear about this. You also have not commented on @mmcdara's analysis. Perhaps you now know how to proceed with the tools at hand and that is the end. But if you want more, some more information about what you know and what you want would seem appropriate. 

@ijuptilk I'm assuming the problem is in the last step. Try adding params=[K[1],mu]. I'll update the other one. Or perhaps Maple is hinting that you should take @sand15's advice :-)