@tomleslie Thank you for checking that, Tom.

I just downloaded Firefox. I explicitly checked boxes during the installation to not set anything and to not import anything. I'm using it right now... and...

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/PiecewiseMerge.mw .

Download PiecewiseMerge.mw

@subzero You wrote:

• The result is assigned to a variable and supressed by (:)

Very glad to hear it.

• The memory usage is now 30%,

It would perhaps be useful to estimate the rate of memory increase. However, many computations reach their peak memory usage long before they are finished.

• the CPU keeps fluctuating between 10% and 99% in short intervals

This mostly depends on the number of cores in use at the time that you're looking. I'd guess that the 10% is 1 core, and the 99% is all of them.

•  I guess the CPU usage is what to worry about here!?

Yes, and what you've described so far is totally normal. If you stop seeing that fluctuation, then you should worry.

• Does Maple make use of multiple cores?

Yes, it's always used for the garbage collection (gc) (which should likely be more properly called memory recycling). Whenever the Time value on the status bar changes, there's just been a gc. That likely accounts for the 99% CPU utilization that you're seeing. The decision to do a gc is based on the quantity of garbage (memory that has been used but that no longer has any current variables pointing to it); it's not based on the time (either real or CPU) since the last gc.

There's a good chance that multiple cores are not used for the computation itself. Most broad-scale algorithms (such as symbolic solutions of equations) are not suitable for parallel processing, and those that are must be very carefully coded to make use of it. Many numeric algorithms are more suited to it.

The problem that you described---a system of 5 order-3 PDEs---sounds immensely complicated to me; I wouldn't be surprised at all if obtaining a symbolic solution would take months of computation. Nor would I be surprised at all if you obtained a solution with RootOfs and integrals so deeply nested that there's no practical way to make use of the result. And you said that they're "overdetermined". I don't have any experience with that. I hope that a pdsolve expert can jump into this conversion and give an opinion on its ability to handle that. You should experiment with a small overdetermined system (I guess two equations in one dependent variable) with a known solution to see how pdsolve reacts to it.

Before I undertake any large computation, I do experiments with quantifiably smaller related problems that are quantified with hueristic metrics that can also be applied to the larger problem. I measure the time and memory usage for the smaller problem and then use statistical extrapolation to predict the time and memory usage for the large problem.

@subzero I don't know whether you'll eventually get a result. The answers that you gave suggest (but don't prove) that it's still doing useful computations. If you choose to let it keep running, keep an eye on the memory usage in Task Manager. If it gets to about 90% of your total, it's hopeless and you should kill it. If the Time stops going up or if that octagon turns gray, let me know. Don't worry about whether the Memory number changes as long as that Time number keeps going up.

Unfortunately, the results could be NULL, and I believe (not sure) that that could mean either that there is no solution or simply that Maple couldn't find the solution.

You should never start any Maple computation in the Standard GUI that can potentially display a lengthy result without doing the following:

• The command should assign its result to a variable;
• The command should suppress its display by ending with a colon (:).

If fail to do this, there's a good chance that if the computation finishes, the GUI will be unable to format the result for display in any reasonable amount of time. This is very unfortunate because it means that you'll not see that result and you'll need to kill your entire Maple session (not just kill the computation kernel) from Task Manager (without being able to save any worksheets!). If that octagon turns gray and Maple isn't responding, that's what's happening. To my mind, this is the most serious design flaw of the Standard GUI because there's no way to save those worksheets. It's hard to believe that they haven't addressed this common and crippling problem after so many years.

@Carl Love Here is a test using Microsoft Edge instead of Google Chrome:

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/PiecewiseMerge.mw .
 

Download PiecewiseMerge.mw

Another (this one is extremely simple):

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/prove.mw .
 

Download prove.mw

The Microsoft Edge is fresh-out-of-the-box, never-been-used, and I didn't import anything from any other browser.

I've seen and read here (other recent threads on MaplePrimes) that the long-standing problem of displaying worksheets inline on MaplePrimes has recently been somewhat "fixed". However, as I reported in the Question above My worksheet-displaying problem is much older than that of other MaplePrimes correspondents and It's absolute, not intermittent: I can't display any worksheet at all, no matter how simple. And now I report that It still doesn't work for me. I use Windows 10 and Google Chrome (always the latest version). I'm not using any unusual settings in Windows, Chrome, or Maple: I think that the only non-default setting in my Chrome is that I never delete history. I use two different computers with that setup, and I have this problem on both.

@subzero Look at the status bar---the bottom right border of the Maple window. What are the values stated for Memory and Time? And has the Time value been updating regularly? Now look at the upper toolbar. In the center, there should be an octagon with an exclamation point (!) in it. Is the octagon red or gray?

If you're using Windows, I'll give you details on using Windows Task Manager to get further information.

@Joe Riel I wasn't suggesting that the compile= false option be eliminated. And surely the name of the file that contains the compiled code could be stored in the library. There must be some way to prevent the need to recompile after every restart. The StringTools package is mostly compiled code.

Usually if an app is not on your "trusted" list, a dialog pops up asking if you trust it. Then you click "yes", or whatever, and you never need to do that again, unless you reinstall the app.

@Ronan Multiplying by (-1)^(m3+1) is equivalent to replacing c3 by -c3 and negating the whole expression. Thus, this'll handle all cases:

restart:
Iterator:-CartesianProduct([1,1]): #Force compilation

P:= 2..4: #suffixes of m and c variables
N:= [$0..4]: #evaluation values of m variables
V:= subs(c3= -c3, [c||P]): #c3= -c3 does nothing if there's no c3 

B:= subs(
    {_C= [$P], _V= V, _S= sign(1-nops(V))}, #sign(0)=1
    proc(M)
    local r:= add(M*~_C), s:= 1+r, t:= s-add(M);
        _S*r!*c0^t*mul(_V^~M)/t!/mul(M!~)/c1^s
    end proc
):
B([m||P]); #to verify formula
#no change below here
CodeTools:-Usage(
    seq[reduce= `+`](B(v), v= Iterator:-CartesianProduct(N$(rhs(P)-1)))
);

How can anyone investigate your Question without knowing the data read into W? You don't need to post the whole file, just the part that's read into W. 

Also, it is possible that undefined is the correct response. I'm not saying at this point that there's any evidence that that's true, just that it's something that's worth keeping in mind. 

@Thomas Richard I consider that as being broken. IIRC, the originally designed purpose of the feature was the immediate quarantining of the main article, all its subthreads, all other threads by the same author, and all future threads by that author.

Let's not forget that in the old days it was common for 20 or so spam to appear from the same author within a few minutes, and I'd delete 50-100 spam every single day. So any deletion process requiring multiple steps is totally unacceptable. If anyone here can't remember how bad it was, that's only because I and a few other Moderators were busy deleting it before those more-casual users saw it.

@Carl Love I've confirmed that Delete As Spam is definitely broken. There's no error message this time; it appears as if it's deleting it; but in the end it's still there.

@Carl Love It may be broken again. Everything on MaplePrimes is unbearably slow right now. There are three new spam Questions (rather than the more-usual Posts) at the moment, 2 of which have spam Replies. I don't know if that's connected to this slowness

For what it's worth, I never close the help window. That's not because I think that I may have some problem reopening it, but rather because closing it seems to me (if I thought about it at all) like a totally unnecessary extra step. But actually it's never occurred to me to close it, although I've always been aware that that was possible, and it's a nuisance to me that I need to reopen it if my Maple crashes.

I'm not at my computer at the moment, but when I have a chance I'll check if I can duplicate what you described. I'm also using Windows 10.

@Carl Love Given procedure B above, the original formula B can be returned (for verification, among other things) by 

B([m||P]);