@acer That's the question. How does one create this input? Maybe it would help if the OP provided an explicit example where this notation is used. I mean a worksheet, not just a reproduction in the body of a message.

@Carl Love I checked ListTools, but forgot that there was a separate ArrayTools.

@Carl Love True. I might be biased, but this looks like some kind of a dynamical system/differential equation. If so, then it's possible the unsolvability of this system indicates an end of the interval of existence of the solution.

Maybe mela (the OP) can give us a little background for this problem, and whether he's surprised that the system is not solvable for T=-0.8.

@mriedel Her's how my home page URL appears in my settings: http://www.math.sc.edu/~meade/

OK. I see. Looking closer you should notice that you have two different epsilons in your expressions. If you look at the Greek palette, you'll see there are two epsilons. If you are working in a 1D input region you'll see that one is "epsilon" and the other is "varepsilon". These are their names in LaTeX.

I changed the epsilon in your definition of per_equation (from epsilon to varepsilon). Now, when all other instances of epsilon are replaced with varepsilon, I get something that might be more along the lines of what you are expecting.

quesiton-answered.mw 

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

I would look to use Maple's textplot command, in the plots package. With this command you tell Maple the coordinates of the point where you want the text to appear.

Here's the first example from the help page for textplot:

textplot([1, 2, "zebra"], 'align' = {'above', 'right'})

You'll probably want to use the align option to move the points a little off the actual data point. But, from your picture I don't see that all of the strings use the same offset, some are above others below, etc.

But, if we have some sample data, I expect someone will be able to help you create a plot similar to the one you included in your original post.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

@anton_dys While thisw would work, it is pretty inefficient - evaluating dsolve each time the function is evaluated.

A better approach would be to use unapply:

u := unapply( rhs(dsolve(...), t );

Doug

Please share the details of what you have tried, either by uploading your worksheet or pasting the code in the body of a post.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

While seeing the specific problem will be helpful, there is one possible quick answer that comes to my mind.

Did you load the MTM package? If Maple spits back your command unevaluated, loading the MTM package should help.

Loading the MTM package is done by executing the command anytime before you execute the ilaplace command:

with( MTM ); 

To test if you have the MTM package loaded, and that ilaplace is working for you, try it on a simple problem:

with( MTM );
ilaplace( 2/(s^2+4) );

If this does not help, please show us the specific problem you are tackling.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

@Carl Love "irreducible results"? Of course you mean "reproducible results", but the slip does have some mathematical humor.

@Doug Meade I should've read your link to "this problem" before responding. I was assuming this was related to "uses" and did not think to recall this GUI bugaboo. Thank you for the careful and complete explanation.

@acer I don't see any changes in your file. (I still see "uses ListTools;") Did you intend to use one of the workarounds I suggested?

@brian bovril I just ran my code in Maple 2015, version 2015.2, and have no problems. To see what version of Maple you are using, use interface( version );, like this:

interface( version );
Standard Worksheet Interface, Maple 2015.2, Windows 7, November 13 2015 Build ID 1087698

If this continues to be a problem, here are two possible workarounds:

1. replace "uses ListTools;" with "use LinearAlgebra in" and insert "end use;" immediately before "end proc:"
2. delete "uses ListTools;" and change "SearchAll" to "ListTools:-SearchAll"

Either of these should give the same functional definition of the LSrecur procedure.

Doug

@rlopez Thanks for the explanation. I sure hope it isn't too difficult to implement a user-controllable setting to allow access to the hidden table.

From a quick look at your example, I think it's important to note that you are talking about a numerical double integral with Digits=32.

Why do you describe your example as a "polynomial sum"? The LaguerreL should be polynomial, but not when evaluated at expressions involving exp and sqrt. Your example starts with 7 terms; after expand it is 359 terms. I also tried simplify,LaguerreL; this removes the LaguerreL but does not change the number of terms in the expression.

In my timings, it took 14 seconds to evaluate the double integral with your "expand"ed integrand. Working with the original integrand took only 9.5 seconds. My best result (9.111 s) was obtained after applying simplify,LaguerreL to the integrand. All 3 results agreed to about 25 decimal places. (See the help page for simplify,LaguerreL.)

When I reduced Digits to 10 (the default), the computation was completed in about half the time. The answer (0.2668399359) agreed with your 32-digit answer to 6 decimal digits - not bad.

If these relative speeds carry over to your full problem, using simplify,LaguerreL could give a 33% improvement, and reducing to 10 digit computations could save another 50% (cutting your overall compute time by a factor of 3).

I hope some of these ideas are of use to you.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu