I'll sign up for this beta testing if at least one person on this list with a reputation higher than mine also signs up. So, if you're signing up, please let me know. Send me email if you want to keep it private.

Or, if any such person has a specific reason why they are not signing up (like, more specific than I'm too busy), please let me know.

I don't understand this line in your code:

B := select(A->abs(A[4])B[5,1]^2+B[5,2]^3+B[5,3]^4; #check

Could you either explain it or correct it?

@amiller Make your very first line of code

restart;

Let me know how that goes! I was able to get the plots, no problem. If it doesn't work, please upload your worksheet directly onto the forum (see the fat green up arrow in the editor). Maybe there are some other inappropriate invisible multiplication signs.

@amiller Make your very first line of code

restart;

Let me know how that goes! I was able to get the plots, no problem. If it doesn't work, please upload your worksheet directly onto the forum (see the fat green up arrow in the editor). Maybe there are some other inappropriate invisible multiplication signs.

@Alejandro Jakubi Thanks. "View page source" works also then. Any idea what causes the long lines? I notice that they are always in a different font---looks like Courier.

If I were to rate various aspects of Maple based on the experience level required to use them, on a scale from 0 to 10, I'd say that using evalhf correctly would be level 3, and using it effectively would be level 4.5. If you're doing symbolic integrations inside an add loop, the savings you get from using evalhf are going to be miniscule. Nonetheless, I will post an answer to your question.

If I were to rate various aspects of Maple based on the experience level required to use them, on a scale from 0 to 10, I'd say that using evalhf correctly would be level 3, and using it effectively would be level 4.5. If you're doing symbolic integrations inside an add loop, the savings you get from using evalhf are going to be miniscule. Nonetheless, I will post an answer to your question.

Your post did not word wrap. I can't read the ends of the last two paragraps. Please repost.

@Axel Vogt 

Yes, I recall writing something like that, but I don't recall posting it. If you saw it, then I did. Someday soon, I'll have to go download all that Yahoo Maple stuff. I haven't looked at it in many years.

The gist of code in question, IIRC, is that if

for integers p, q, m, n with q = 1, 5, 7, or 11, then the trig functions of θ can be expressed in (complex) radicals. I can't recall if my code handled every case.

The case q = 11 is quite interesting because it involves solving a quintic. I wonder if there are higher values of q for which the polynomial is solvable (even though Maple can't solve it). Does anyone here know? For q odd, the polynomial to solve for is of the form where degree(p) = (q-1)/2 and all the roots are real and in (0,1).

What if q is a Fermat prime? For q=17, that polynomial is degree 8. Maple should be able to compute the galois group, but I don't know how to interpret the results. Seems like there should be a connection between this and Gauss's proof of the compass-and-straight-edge constructability of a regular n-gon when n is a Fermat prime. (Gauss's wanted his tombstone to be engraved with a regular 17-gon.)

It's not so simple. You used 12 instead of 16. Try it with 16.

It's not so simple. You used 12 instead of 16. Try it with 16.

@Markiyan Hirnyk The Maple approach is a sledgehammer that I don't like because it involves checking 2^15 cases to do something that should be (at least in principle) doable with secondary-school combinatorics. But I had to find out where my analysis went wrong.

@Markiyan Hirnyk The Maple approach is a sledgehammer that I don't like because it involves checking 2^15 cases to do something that should be (at least in principle) doable with secondary-school combinatorics. But I had to find out where my analysis went wrong.

I could show you how to do it with evalhf, but it is a little complicated. So, first I ask Did you mean evalf? I don't see any benefit to using evalhf in this case. So let me know if you really want evalhf, and why.

@Joe Riel Finally, I get it! Thank you for your patient explanation. Put more succintly (I think), in all cases I was missing the choice of whether the element(s) of (A xor B) were or were not in C. In the |AB|=4 case, there is one such element, for a factor of 2; in the |AB|=3 case, there are two such elements, for a factor of 2^2.

I editted my solution at the top of this subthread to reflect these corrections.