@Joe Riel I would only trust that method if I knew how many roots there were. I have had cases where the fsolve starts to return unevaluated even though there are still roots to be found.

It looks like a right angle to me also. Get a ruler and measure the grid spacing.

@Kitonum The source of the bug is that you forgot to make x and y local.

@Kitonum I also get true for Markiyan's example. This must have something to do with a version change in Maple.

@brian bovril 

On Windows, create a plain text file named maple.ini and put it in C:/Program Files/Maple 17/Users. You can put any Maple commands in this file. What I have is

Digits:= 15;
kernelopts(opaquemodules= false);
interface(rtablesize= 30);
interface(prompt= "");
libname:= libname, "C:/Maple_packages";

@Shanobadur 

Detecting repeated vertices is easy:

SignedArea := proc(Pts::list([algebraic,algebraic]))
local i, P:= [Pts[], Pts[1]];
     if nops(Pts) <> nops({Pts[]}) then return 0 end if;
     add(P[i][1]*P[i+1][2]-P[i+1][1]*P[i][2], i=1..nops(Pts))/2;
end proc:

@nm The operands of [[1,2],[3,4]] are [1,2] and [3,4]. So map(igcd, [[1,2],[3,4]]) is equivalent to [igcd([1,2]), igcd([3,4])]. This doesn't work because igcd doesn't take a list as an argument. You are confusing extracting the operands of [[1,2],[3,4]] with extracting the operands of [1,2] and [3,4].

Is that sufficient explanation?

@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.