x:= [2,3,5,1,4]:
y:= [1,2,3,4,5]:
H:= table(x =~ y):
convert(H, list);
 

The default built-in ordering that sort uses for listlists is lexicographic, so the following works and is more efficient than sorting with a user-supplied total-ordering procedure:

sort([[2,1],[3,2],[5,3],[1,4],[4,5]]);

                  [[1, 4], [2, 1], [3, 2], [4, 5], [5, 3]]

@Joe Riel Oh, I just misunderstood your last sentence to mean that the attributes trick could be done simpler, faster, and smaller in a loop. You just meant a straightforward max-finding loop. It's all clear now.

Please repost the array Data in a plaintext form so that I can cut-and-paste it.

@Joe Riel I'm having trouble understanding your last sentence---why it's simpler, faster, smaller. Could you show an example doing it in a do loop?

It just requires a slight modification of the original:

add(s^LL[1]*t^LL[2]/mul(x!, x= LL), LL= L);

@reemeaaaah I see what's wrong. When you typed into MaplePrimes, you typed B1:= ..., B2:= ..., but that should've been B[1], B[2]---indicating a subscripted variable. Change the sort to

sort([seq(B[k], k= 1..n)], (A,B)-> (A[2]-A[1]) > (B[2]-B[1]))[1];

@Kitonum Your comparison is invalid because the sums in the first plot command are being evaluated to exp(z)*w. For a valid comparison you need to use Sum (not sure it will work) or do something else to evaluate the sums numerically.

The exp(z)*w is obviously wrong. Just divide both sides by w, and then the sum depends on w while the other side does not.

I created tag "hypergeom" and applied it to your Question.

@J4James I can get portions of the above graph, but I am having trouble solving the BVP for b > 16. I get error message "Newton iteration is not converging". I am trying to adjust the numerous parameters to dsolve. Here is what I have so far (this plots a wider range than my first):

Eq:= diff(f(y),y$3) + f(y)*diff(f(y),y$2) - diff(f(y),y$1)^2 -
     c*S*(diff(f(y),y$1) + y/2*diff(f(y),y$2))=0:
bc:= D(f)(0)=1, f(0)=0, (D@@2)(f)(b)=0:

F:= proc(_b, _S)
local Sol;
     try
          Sol:= dsolve(eval({Eq,bc}, {S= _S, b= _b}), f(y), numeric, continuation= c);
     catch:
          userinfo(1, F, StringTools:-FormatMessage(lastexception[2..-1]));
          error
     end try;
     eval(f(y), Sol(_b)) - _S*_b/2
end proc:
     
infolevel[F]:= 1:

Note the inclusion of continuation parameter c in Eq.

Don't use the above for b=0 because then it's an IVP not a BVP and different coding is required.

@nm You wrote:

fouriercos(F(x),x,w);

That should be F(w), not F(x).

I believe that what Axel was saying is that fouriercos is its own inverse.

@AlStiegman 

Is your version of Maple before Maple 13? Then replace

{vars} =~ 0..1

with

map(`=`, {vars}, 0..1)

To plot just a single variable, use

plot([seq([TT(j), eval(x, Sols[j])], j= 0..10)]);

@AlStiegman 

You can do the five plots together like this:

vars:= w,v,x,y,z:
TT:= j-> 800+10*j;
for j from 0 to 10 by 1 do
     T:= TT(j);
     Sols[j]:= fsolve({fsc, fbd, fhc, fmassbal, fmb}, {vars} =~ 0..1)
end do:

plot(
     [seq([seq([TT(j), eval(V, Sols[j])], j= 0..10)], V= [vars])],
     color= [black, red, green, blue, brown], legend= [vars]
);

@kminor2578 This is not your fault, but the file didn't upload. This is a known bug in MaplePrimes.

Your post is missing the equations. Try attaching a worksheet to a Reply.