@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 :-)

@mmcdara Nice analysis. For the case where you postmultiplied the Gram Schmidt matrix by DiagonalMatrix( [1$(N-1), T*sign(d)]) you have scaled the last column by magnitude T, so they are random but with a different range from the other columns. Your next example solves that problem.

I was trying to work an integer case based on GS.DiagonalMatrix( [1$(N-1), T]).GS^+ (which solves the above problem, I think), but if T=1, then you get the identity matrix, which suddenly is not very random, even though T<>1 looks random. This made me wonder if the entries of GS itself are too correlated to be random, but that is beyond my limited statistics expertise.

@lcz Tarjan's algorithm seems to be standard, and was for directed graphs, (but works also for undirected if allowance is made for the double counting). So, yes it is strange not to have the capability for both.

It was the fastest of the algorithms I played with, but perhaps with dense graphs other algorithms might be better. Tarjans's could probably be converted to a compiled version in Maple, if the stack was implemented "by hand" using arrays. I was originally thinking algorithms based on cycle basis was the way to go, but the literature doesn't seem to point to that.

I also have another version that uses Zeon algebra, but just counts and doesn't produce the cycles themselves, so I added it to the other thread:

How-To-Determine-The-Number-Of-Cycles-Of--Graph

Infolevel gives information that is not that enlightening. 

solve.mw

I can't decide whether this is a bug, or whether we are expected to be cautious when mathematical functions like ln are involved.