@Markiyan Hirnyk Your test range is too small to detect the difference. The differences that you are seeing are just noise. Try this

CodeTools:-Usage({seq(13^k mod 100, k= 1..100000)}):
memory used=4.32GiB, alloc change=9.37MiB, cpu time=41.67s, real time=41.34s

CodeTools:-Usage({seq(13 &^ k mod 100, k= 1..100000)}):
memory used=8.40MiB, alloc change=0 bytes, cpu time=157.00ms, real time=143.00ms

@Kitonum Note the difference in efficiency between 13^k mod 100 and 13 &^ k mod 100.

@J4James That's the point of the exercise: contrast. Procedures and expressions are different. In eval(f), the x is a procedure parameter, and it is not affected by the assignment to global x.

The presence of a subscript is insignificant. You'll get the same error if you use just P^q+R^q.

@Durre 

1. There is no practical difference between evalf(Int(...)) and int(..., numeric). I think that the former is the more common usage.

2. I picked _d01ajc because the help said that it was for badly behaved integrands. I guess if _d01akc works, you can use it.

@Joe Riel I thought that he meant 4 groups with 7 members each.

@Luka A vector can be considered a 1 x n matrix.

Only square matrices have eigenvectors, but the eigenvectors themselves are not square.

@brian bovril As long as the number of groups is a power of two, the divide-and-conquer approach will work. It doesn't matter what the number of numbers is.

@Andriy 

The time savings effected by the various ways of declaring the Matrix are minuscule compared with the time taken by elem. Thus the measurement of those savings is lost in the "noise" of the measurement of the overall time. As shown in an example at ?Fortran_order , the savings from scanning a 2000 x 2000 Matrix in the correct order is slightly less than 0.1 s. Thus the savings from scanning a 500 x 500 Matrix in the correct order wouldn't even be measurable. The smallest measurable time in Maple is 1/64 s.

@Andriy Agreed on all points. I can see that you already have much understanding of these matters.

What is the data type of the entries? (integer, rational, float, polynomial, etc.)

How much savings are you getting (in percentage real time) by using Threads? The sequential code to compare with is not your original loops, but rather the automatic fill

st:= time[real]():  A:= Matrix(N, N, elem, shape= symmetric):  time[real]()-st;

And what is your value of kernelopts(numcpus)?

@brian bovril 

Rather than altering the code, it is easy to do the labeling with post-processing:

L:= [1829.0, 1644.0, 1594.0, 1576.0, 1520.0, 1477.0, 1477.00, 1404.0
      , 1392.0, 1325.0, 1313.0, 1297.0, 1292.0, 1277.0, 1249.0, 1236.0]:
Labels:= [A||(1..nops(L))]:
L_ind:= Var(L, 4, 4): #Call Joe's procedure
subsindets(L_ind, posint, k-> L[k]);
              [[1829.0, 1392.0, 1292.0, 1249.0],
                [1644.0, 1576.0, 1277.0, 1236.0],
                [1594.0, 1477.0, 1325.0, 1313.0],
                [1520.0, 1477.00, 1404.0, 1297.0]]

subsindets(L_ind, posint, k-> Labels[k]);
 [[A1, A9, A13, A15], [A2, A4, A14, A16], [A3, A6, A10, A11],
   [A5, A7, A8, A12]]

@Andriy Sorry, I forgot the angle brackets. Change the second-to-last line to

A[i,..]:= < Threads:-Seq(Elem(i,j), j= 1..N) >

(I corrected the original.)

In your real code, is elem also something trivial, timewise?

@Kitonum How can there be two answers?

@Mac Dude You can "pin" it by clicking on the box of stars in upper right corner of the post, immediately under the box with the "thumb up" where the votes are recorded. This saves it to your list of favorites which can be accessed from your profile.

I edited the tags in your post, hoping that Edgardo would notice.

Maple 17 is a software package, the current version of Maple. MaplePrimes is this forum that we are posting on, where Maple and related packages are discussed.