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. 

I'm not sure about this, but it seems that you may be conflating external compiled code with evalhf'able code.

@hojat Please post the exact error message, or upload a worksheet showing it. While the words "could not store" may appear in the new error, I doubt that the mathematical expression shown is the same.

The three most likely causes of this error are

1. A misspelled variable name which Maple cannot convert to a numeric value.
2. A variable that you intended to assign a numeric value to, but you forgot to.
3. The presence of small nonzero imaginary parts due to decimal round-off error in a context (such as minimization) where real numbers are required. 

All of these are usually easy to correct.

I think that acer's Answer is better than mine, and had I seen it before I wrote mine, I wouldn't have answered.

@lcz The paper that I referred to above is one that you posted a link to in a previous thread:

1. Marthe Bonamy, Oscar Defrain, Marc Heinrich, Michał Pilipczuk, and Jean-Florent Raymond. Enumerating minimal dominating sets in K_t-free graphs and variants. arXiv 1810.00789

@mmcdara Yes, that is why I knew that example off the top of my head.

Regarding your question from your last paragraph: The first argument of Eval can be anything:

Eval(A, x= b);

The A could be replaced by any expression. There is nothing worth documenting about the case where A is a D expression.

You need to choose as c integers that can be represented in multiple ways as a sum of two 4th powers of integers. Those c are rare. For context, the smallest integer that can be represented in two distinct ways as a sum of two 3rd powers of positive integers is 1729.

I think that the smallest possible c is

635318657 = 59^4 + 158^4 = 133^4 + 134^4,

which I found by brute-force search of all sums of 4th powers of distinct positive integers <= 200:

select[flatten](
    x-> nops(x)>1, 
    ListTools:-Classify(`+`@op, combinat:-choose([$200]^~4, 2))
);

And I'm not saying that this c will work, just that it's the smallest c for which there's even a chance.

Your update from today, with significant bug-producing examples, is quite important. I totally missed it when I reread this thread some hours ago. Note that MaplePrimes does not change the date in the top right corner of any post. You should repost that as a new Reply to the Question so that it gets its own date and hopefully wider readership.

Is there some good reason why your code is nearly identical to the code in the current basins-of-attraction Question thread initiated by @Danish Toheed?