I don't understand the probability split (1/7, 8/21). I think that you made a typo, and that that was meant to be (3/11, 8/11). So, you could improve the code by including an automatic check that the sum at each node is 1.

@C_R I'm not sure here, but I think that the problem that you're describing is that plots as a whole appear too small on very high resolution displays (such as QHD). But I think that the OP's problem is only that the fonts in the plots appear too small.

I've noticed for years that the symbol for unary negation in prettyprinted output is often (but not always) absurdly long and sticks out like a sore thumb. I'd also prefer it to be moved to the right, closer to its operand. When I read these, for a fraction of a second I mistake it for a binary operator with a missing (or NULL) left operand.

What do you think the height of the unary negation operator should be? I think somewhere between 1/4 to 1/3 of a line-space down from the top line would be best. Currently it's halfway down, which also contributes to it looking like a binary rather than an unary operator. 

@Carl Love The comments and expository introductory text of my originally posted worksheet above incorrectly used the graph-theory term minimal dominating set where I should've used minimum dominating set. Although it offends my sense of English grammar---which says that minimal is nothing more than the adjectival form of the noun minimum---the usage of these as distinct terms in graph theory is apparently well established. A minimum dominating set of a graph G is a dominating set of the smallest size of any dominating set of G. A minimal dominating set is one no proper subset of which is a dominating set of G. (Thus, a minimum dominating set is necessarily minimal, but not the converse.)

This error was only in my text and comments; there was no error in the code.

I also added a proof of the fundamental proposition that makes my algorithm work.    

@ecterrab Yes, it may be desirable to document that AllSolutions was required to get the output. I feel that that has been handled adequately by the input syntax. The output is meant to be a more-standard typeset mathematical display, and AllSolutions is Maple-specific syntax, not standard typeset math.

Do you just need to generate some random examples of the matrices with the given determinant? Or do you need them to be "fairly" chosen, e.g., each matrix with that determinant is equally likely to be chosen? What is the algebraic category of the matrix entries: integer, rational, finite field, etc.? 

@Timm Thaler Okay, asking for the radius of convergence with respect to free R makes sense. You originally had a specific value for R, making it not free. Using B=5 and N=1, I've tried elementary techniques such as the root test and ratio test, but I haven't found anything that works yet. 

So, I'm answering the OP's anticipated followup question before it's even formally posted:

Your series doesn't have any free variables. Neither the concept of radius of convergence nor power series makes sense without a free variable. Your series is simply a real constant; it's not a function, except in the trivial sense of a constant function. 

You can make a variable free if you want, and then ask again. The only variable whose "freedom" would make it a power series is R.

@MANUTTM Yeah, I already knew what you want. It's a much-deeper question than the simple syntax issue with the parentheses. I don't feel like working on it at the moment.

This is @mmcdara's Reply that I accidentally separated from this thread:

@ecterrab 

Thanks for your comment.
I kind of like your "if the new topic really interests me" which emphasizes on personal satisfaction before, say, overall gain for the Maple community. This is also one of my motivation.

By the way I wonder if I wouldn't have done better to create a post rather than a question?

Sorry, I wanted to make this thread a Post (even before seeing your comment about that), but I clicked on the wrong thing and made only your latest Reply a Post. There's no way that I can undo that without making it look like I am the author of the Reply. But you can do it with copy & paste.

In my opinion, requests for open discussion of topics / questions for which there can be no definitive answer should be Posts.

@delvin If you post a Reply here, that moves this thread to the top of the Active Conversations tab; so it makes it just as visible as posting a new Question.

You should post your worksheet here because I guarantee you that I'll never look at a *.docx file.

@Zeineb The problem asks you whether there is a ring homomorphism from E to F. I haven't answered that. I merely wanted to steer you away from the incorrect idea that both E and F were fields. I suggest that you consider a function E -> F that isn't a bijection.

Letting F11 be the field with 11 elements, you define E = F11[x]/(x^2 - 5) and F = F11[x]/(x^2 - 2). F is a field, but E is not, because x^2 - 5 is reducible over F11, its roots being 4 and 7.

@sursumCorda It seems to me that the term "lexical scoping" on the help pages that you linked is being used with a different meaning than the dichotomy "lexical scoping" versus "dynamic scoping" that we're discussing here. I think that that help page is actually talking about lexical variables (not as a dichotomy) rather than lexical scoping. As the test code that I posted above shows, even Maple's lexical variables are dynamically scoped.

Although those help-page examples still work perfectly as presented, it should be noted that they're about 23 years old and were written before the existence of modules or any formal mechanism for object-oriented programming.