@nm In ~set, it is a completely different use of ~ than an elementwise operator. The ~set is a coercion procedure (see ?coercion ). It is used to force a conversion from other data types into a set. IfT is any type name, then you can write a procedure ~T that converts other types to T. Then you can use ~T as a type in a procedure's parameter declarations. When that procedure is passed an argument that is not of type T, then procedure ~T is applied to that argument.

Is that sufficient explanation?

@Markiyan Hirnyk What if the sample was of size 30 or larger? If we have a large (possibly infinite) stream of selections from combinat:-choose(8,5), how can we decide whether the selections are done uniformly at random? Such a process must be used to test the randomness of a lotto machine.

@J4James Sorry, I don't have free access to the article. I am sending you email so that you can send me the PDF attached to an email.

@JohnS Thanks for the compliment. I just added some comments to the above to try to explain exactly what the code is doing.

@J4James Darn it, the link to the PDF doesn't work. Not your fault; it's the "upgrade". Attached files seem to work intermittently. Do you have a URL for the PDF?

@J4James Do you know that the parameters Pr, c, and N are the same for the other plot?

@J4James Okay, I understand what you did to get Nux. And, as far as I can tell, you made no mistakes in transcribing the old system to the new. Now, what is the plot that you are comparing it to? I know that you posted it before, but I can't find it. It may have been a victim of the recent "upgrade". So please post it again.

@awass The multiple-email bug has been fixed.

What you want should be easily achievable by some small modifications to procedure `print/Unit`. Simply removing the square brackets is as easy as

`print/Unit`:= ()-> args;

Adding the color and uprightness should be possible with the Typesetting package, but I don't know the details. I don't know about changing the spacing.

One might as well "endcap" the list right in the procedure:

SignedArea := proc(Pts::list([realcons,realcons]))
local i, P:= [Pts[], Pts[1]];
     add(P[i][1]*P[i+1][2]-P[i+1][1]*P[i][2], i=1..nops(Pts))/2;
end proc:

Now, the bigger challenge is How to detect nonsimplicity of the polygon?

@peardrop How can they be considered linear equations if the a, b, c, d are functions of x[1], ..., x[60]?

@cmcjas Perhaps this will help: i goes from 1 to n. Plugging i = 1 into (i-1)*dxj+a yields a, which is the leftmost point in the first (leftmost) subinterval. Plugging i = n into i*dxj+a yields n*(b-a)/n+a = b -a + a = b, which is the rightmost point in the last (rightmost) subinterval. How's that?

Do you mean that you want to construct a surface from 27 points using c1 = x coordinate, c2 = y coordinate, and c3 = z coordinate?

@J4James No, I don't know how to handle this. In particular, I don't know how you got sys from {Eq1, Eq2, Eq3}. Where does Nux come from? I wonder if there was some mistake made in this process.

What do mean that they are functions of x? Is x distinct from x[1], x[2], ..., x[60]?