@Stretto I did not understand what you wanted from the grid lines from your original Question. You must admit that "grid lines [that] nicely project from the function" is nowhere near as precise as what you said immediately above. What is the purpose of the eight corner pieces on your grid lines---the parts that are essentially perpendicular to the main grid liines? Please show the code for the gridlines above, which are much better than those in your original Question.

@Joe Riel Thanks, I didn't know that an rtable could be indexed by another rtable or by NULL (rather than ..).

Is the intermediary B necessary for efficiency? Because the following seems to do the same thing:

A:= Array([a,b,c,d,e]): # Array of elements to permute
for p in Iterator:-Permute(numelems(A)) do
    printf("%{}a\n", A(p));    # print (replace with something useful)
end do:

For the tough cases, a Monte Carlo algorithm for piecewise linearity would be to evaluate the second derivative at a few randomly chosen values of the with-respect-to variable. 

@vv Your example thus makes it clear that the overall question of linearity is in general undecidable because the boolean condition in the piecewise could be made undecidable.

@Scot Gould No worries; typos happen to us all. On MaplePrimes, I can almost always figure out the intended meaning, but this time the "is" threw me off (especially since there is an is command in Maple).

@Scot Gould Thank you, I understand now. Your original second paragraph refers to an "is" feature. I'm guessing that that was a typo (which you can edit from the "More" pull-down in the bottom right corner).

@Scot Gould I agree. Explore is a great feature. And it can also be used for commands other than plots. 

Would you please edit your second paragraph for clarity?

@Kitonum You need to explain where you got the "magic numbers" 115, 257, and 231, because they would likely be different for other curves. I can see where 257 and 231 came from, but this may not be clear to the OP. You can always use -1 for the last index.

@Carl Love There's another sophisticated memory-management technique, which I didn't mention earlier, called weak tables. These are new to Maple 2019, and they're documented on help page ?table,weak. Basically, an item stored in a weak table gets garbage collected when there are no pointers to it other than the table itself. There are a few distinctions between items stored in the indices and those stored in the entries that you should read about on the help page.

As far as I can tell, there's no way to make the automatic remember table of a procedure a weak table, although it seems like that would be a great use for them.

Thanks, that's a clearer explanation of the problem. I think that in the other PDF, n and s were switched in some instances, and the matrix A was confused with the coefficient matrix A(t) of the IVP. Likewise, you should distinguish b from b(t) by using a differrent letter. The two vectors are not related, and not even necessarily the same size.

There's no significant benefit to making M constant rather than a function of t.

@num211 Please post this as a new Question. PDF format is fine. Any supplementary material that you can provide would be helpful (such as how to choose n). At first glance, the proposed method seems like doing a great amount of computation to get just one point of the solution (i.e., one value of t) for a linear IVP---a problem for which there are already several great algorithms, such as RKF45. 

@tomleslie I like your way of combining a colored wireframe with its corresponding surface. 

@Kitonum If your two (likely rhetorical) questions were directed at me: After making a few very minor corrections to the OP's code so that I could see the plots, I decided to color the plot's own gridlines to replace the OP's idea of drawing the gridlines with spacecurve. I think that this produced a much better plot than the OP's, while still retaining their basic structure, including coloring function. I modified the coloring function for the grid so that it would contrast. 

The OP has imaginaryunit reset to _i in their initialization file.

I like your plot.

@Kitonum Thanks. My results conform with yours if I change the initial value of t from 1 to 0. I made that initial value user-specifiable.

@Kitonum From the way that the OP has phrased the Question, it's clear (to me at least) that the solution is wanted in a matrix and vector form. They also implied (although, not clearly) that they already know how to get the dsolve solution. 

I'd have no objection to a dsolve Answer that didn't use DEtools:-matrixDE if that Answer produced a Matrix and Vector form.