That definition of T(x) should be enough. But your initial conditions are ill-posed:

R(x) = 0, X(x) = 10;

Shall I assume that that should be
R(0) = 0, X(0) = 10
?

That definition of T(x) should be enough. But your initial conditions are ill-posed:

R(x) = 0, X(x) = 10;

Shall I assume that that should be
R(0) = 0, X(0) = 10
?

Another great algorithm, Kitonum. As a point of reference, these structures are formally called (in English) "polyominoes" (rather than "polygons of the match"), and there is much literature on them.

Could you please edit the first paragraph of your post?  The right sides of the lines are cut off; they did not word wrap.

And how did you export an array of plots from Maple? Perhaps by using an external plotter? When I try (in Standard GUI), it only lets me select one cell.

@Markiyan Hirnyk Well, of course, that's just -ln(2). But that is the only point in the plot range that plot was able to evaluate. You can see that in the plot structure:

P:= plot(F, k= 0..2):  # F cut-and-paste from OP's warning msg.
op(P);

CURVES(Matrix(2, 2, {(1, 2) = -.693147180559945, (2, 1) = HFloat(HFloat(undefined)), (2, 2) = HFloat(HFloat(undefined))}, datatype = float[8], storage = rectangular, order = Fortran_order, shape = []), COLOUR(RGB, .47058824, 0., 0.54901961e-1, _ATTRIBUTE("source" = "mathdefault"))), AXESLABELS(k, ""), VIEW(0. .. 2., DEFAULT, _ATTRIBUTE("source" = "mathdefault"))

For every other value of k that plot tried, it got the error about abs not being differentiable, but it traps those errors in a try ... end try block. It won't draw a curve with only one point, so it just displays empty axes.

@Markiyan Hirnyk Well, of course, that's just -ln(2). But that is the only point in the plot range that plot was able to evaluate. You can see that in the plot structure:

P:= plot(F, k= 0..2):  # F cut-and-paste from OP's warning msg.
op(P);

CURVES(Matrix(2, 2, {(1, 2) = -.693147180559945, (2, 1) = HFloat(HFloat(undefined)), (2, 2) = HFloat(HFloat(undefined))}, datatype = float[8], storage = rectangular, order = Fortran_order, shape = []), COLOUR(RGB, .47058824, 0., 0.54901961e-1, _ATTRIBUTE("source" = "mathdefault"))), AXESLABELS(k, ""), VIEW(0. .. 2., DEFAULT, _ATTRIBUTE("source" = "mathdefault"))

For every other value of k that plot tried, it got the error about abs not being differentiable, but it traps those errors in a try ... end try block. It won't draw a curve with only one point, so it just displays empty axes.

@Markiyan Hirnyk I realize that my plot is not what the OP was trying to plot. I was trying to illustrate that the warning message was unrelated to the failure to get a plot. Rather, the issue is as Preben suggested: the inability to evaluate the derivative of abs that appears in the OP's function.

@Markiyan Hirnyk I realize that my plot is not what the OP was trying to plot. I was trying to illustrate that the warning message was unrelated to the failure to get a plot. Rather, the issue is as Preben suggested: the inability to evaluate the derivative of abs that appears in the OP's function.

@Markiyan Hirnyk If you were asking the question to be Socratic with the OP, then I am sorry for interfering here. But if you really were asking because you didn't understand the OP's problem, then C = Limit(z(t), t= infinity).

@Joe Riel I'm glad you switched to using has. Your prior procedure for backtracking for the previously used vertices was taking the vast majority of your cpu time. I will run a comparison.

Edit: I ran the comparison, and your most recent linked-list version does use less memory. The run times are about the same, more-or-less depending on when the garbage collection kicks in. I'll have to run with some bigger examples to even out the gc()s.

One potential drawback to the linked lists is the need to flatten them for most practical uses.

@Joe Riel I'm glad you switched to using has. Your prior procedure for backtracking for the previously used vertices was taking the vast majority of your cpu time. I will run a comparison.

Edit: I ran the comparison, and your most recent linked-list version does use less memory. The run times are about the same, more-or-less depending on when the garbage collection kicks in. I'll have to run with some bigger examples to even out the gc()s.

One potential drawback to the linked lists is the need to flatten them for most practical uses.

I don't think that there is any easy way to add a second horizontal axis. You'd just have to fake it by plotting line segments and using textplot for the tickmark labels. However, note that the tickmarks and the tickmark labels on any actual axis can be changed relatively easily. What is printed for the tickmark labels does not need to correspond numerically to what is in the plot. Indeed, the tickmark labels don't even have to be numbers. So, you could modify the one existing horizontal axis to reflect whatever scale you want.

If you wish to persue this, please post the question in a fresh thread.

I don't think that there is any easy way to add a second horizontal axis. You'd just have to fake it by plotting line segments and using textplot for the tickmark labels. However, note that the tickmarks and the tickmark labels on any actual axis can be changed relatively easily. What is printed for the tickmark labels does not need to correspond numerically to what is in the plot. Indeed, the tickmark labels don't even have to be numbers. So, you could modify the one existing horizontal axis to reflect whatever scale you want.

If you wish to persue this, please post the question in a fresh thread.

@Markiyan Hirnyk I spent a few hours thinking about the problem while washing dishes and doing laundry. Mostly I thought about how I could apply the LogicProblem package to it. I am very familiar with that package, because I wrote it. But I have not used it in eight years, so the details are not sharp in my mind. Eventually I decided that this problem was not suited for that package.

I view this problem immediately as a combinatorics problem---more specialized than simply logic. Combinatorics is very close to graph theory. Also, the symmetry of 12 and 5 together is very appealing to me (think of dodecahedra). Once I considered using graph theory, the way to do the problem was obvious to me.

How did you do the problem? Finding 3-cliques in this problem is easy, even just by hand and without using a graph. The hard thing is proving that there are no 4-cliques.

@Markiyan Hirnyk I spent a few hours thinking about the problem while washing dishes and doing laundry. Mostly I thought about how I could apply the LogicProblem package to it. I am very familiar with that package, because I wrote it. But I have not used it in eight years, so the details are not sharp in my mind. Eventually I decided that this problem was not suited for that package.

I view this problem immediately as a combinatorics problem---more specialized than simply logic. Combinatorics is very close to graph theory. Also, the symmetry of 12 and 5 together is very appealing to me (think of dodecahedra). Once I considered using graph theory, the way to do the problem was obvious to me.

How did you do the problem? Finding 3-cliques in this problem is easy, even just by hand and without using a graph. The hard thing is proving that there are no 4-cliques.

@arctica1963 Your expression for Zsubload has an extra factor of "rho". Take out the (rhoload - rhowater) in front. Note that each term of the complicated coefficient at the end already contains a "rho" factor.

Just a guess, but do these formulae have to do with airplane radio interference caused by power transmission cables?