@Markiyan Hirnyk

That generates the sample space, in a sense, but not in a way that is helpful for solving the problem, because your sample space is far from equiprobable. To see this, consider a problem with much smaller numbers:

A box contains two white balls and one black ball. Two balls are selected at random without replacement. What is the probability that both selected balls are white?

Using combinat:-choose in list mode gives us:

combinat:-choose([w,w,b], 2);

[[b, w], [w, w]]

If we assume, incorrectly, that this is an equiprobable sample space, we get the wrong answer, 1/2. And if we don't make that assumption, then generating the sample space does not help in getting a numeric answer to the problem.

We can generate an equiprobable sample space by using choose in set mode:

combinat:-choose({w1,w2,b}, 2);

{{b, w1}, {b, w2}, {w1, w2}}

from which we see that the answer is 1/3.

For the OP's problem, it is infeasible to generate the equiprobable sample space (nor did the problem ask for that), as it has (52 C 9) ~ 4 billion elements.

Thanks. I haven't tried the copy/paste, although I've seen that you can select the whole array. Where would I paste it? And what would the format (GIF, JPG, etc.) be? My immediate desire is to upload to MaplePrimes, but FireFox (my web browser) only allows pasting plaintext to MaplePrimes.

Thanks. I haven't tried the copy/paste, although I've seen that you can select the whole array. Where would I paste it? And what would the format (GIF, JPG, etc.) be? My immediate desire is to upload to MaplePrimes, but FireFox (my web browser) only allows pasting plaintext to MaplePrimes.

I managed to figure out what your original post meant, but I can't make sense of this. How about trying to do what you want in a worksheet and uploading the results?

I managed to figure out what your original post meant, but I can't make sense of this. How about trying to do what you want in a worksheet and uploading the results?

To answer your second question---about multiple functions on the same graph: Yes, all that is easily done with plots:-display. See ?PlottingGuide. For a complete answer, post your question in a separate thread.

To answer your second question---about multiple functions on the same graph: Yes, all that is easily done with plots:-display. See ?PlottingGuide. For a complete answer, post your question in a separate thread.

@brian bovril Do you mean all the factorings of 36 into 3 parts? The program under discussion in this thread does not consider 1 to be a part of any factoring, but the results could be easily modified to include 1. Just take all the factorings, Factorings(36,1), Factorings(36,2), and Factorings(36,3), and pad the results with the appropriate number of 1s.

@Markiyan Hirnyk I'm not try to prove anything about the expression F in the mathematical sense of proof. I'm trying to prove, if you could call it that, or verify, that plot was unable to evaluate F at any of the values that it chose, except for k = 0. It may well be that there are other values of k at which F can be evaluated.

Now I am convinced that this situation---where plot can only evaluate the expression at one value---should be considered a bug, because it should give the same warning message that one gets if it can't evaluate the expression at any values. Displaying empty axes with no warning is not helpful.

Compare plot(1+x*I, x= 0..1) with plot(1+x*I, x= 1..2).

@Markiyan Hirnyk I'm not try to prove anything about the expression F in the mathematical sense of proof. I'm trying to prove, if you could call it that, or verify, that plot was unable to evaluate F at any of the values that it chose, except for k = 0. It may well be that there are other values of k at which F can be evaluated.

Now I am convinced that this situation---where plot can only evaluate the expression at one value---should be considered a bug, because it should give the same warning message that one gets if it can't evaluate the expression at any values. Displaying empty axes with no warning is not helpful.

Compare plot(1+x*I, x= 0..1) with plot(1+x*I, x= 1..2).

PDEtools:-Solve just passes the problem on to dsolve if it detects that they're ODEs. If dsolve is used for this problem without the numeric option, it will spend a huge amount of time and memory trying to find a symbolic solution. I didn't let it finish, as I was getting close to my memory limit.

PDEtools:-Solve just passes the problem on to dsolve if it detects that they're ODEs. If dsolve is used for this problem without the numeric option, it will spend a huge amount of time and memory trying to find a symbolic solution. I didn't let it finish, as I was getting close to my memory limit.

@spradlig

Plain text is easiest to work with. Use one of the three clipboard icons on the toolbar in MaplePrimes to cut-and-paste directly into your post. Maple understands plaintext, but not Word AFAIK. Or upload a worksheet. Why take the extra step of going through Word?

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@spradlig

Plain text is easiest to work with. Use one of the three clipboard icons on the toolbar in MaplePrimes to cut-and-paste directly into your post. Maple understands plaintext, but not Word AFAIK. Or upload a worksheet. Why take the extra step of going through Word?

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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
?