@J F Ogilvie The name of the command is applyrule; apply is a separate command. You have

apply(Rule, %);

which should be

applyrule(Rule, %);

@sarra 

It is natural for you to try what you did, but it doesn't work because a series is a special data structure in Maple, which can't be simplified by the normal rules. You can use convert(eq7, polynom), but this eliminates the O order terms. You will need to add back O(h^3) manually. Note that O doesn't obey normal arithmetic: O(h^3) - O(h^3) is still O(h^3) rather than zero or O(0). All this is why I recommended the simple form

y(x+h) - y(x-h):  % = series(%, h=0, 3);

The series command (and other commands that produce the series data structure, such as taylor) understands the special rules about O, but other commands do not.

@acer

Thanks for the information about in! I usually use = because it's fewer characters, but now this small difference in timing and large difference in memory requires more investigation.

For large-scale use of parse for digit conversion you should probably use a table:

Parse:= proc()  option remember;  parse(args)  end proc:

Since Maple 18 has just been announced, I'd like to point out a new feature that is relevant to your analysis: CodeTools:-Usage now reports garbage collection time as a separate category.

F1:= proc(x)
local y;
     y:= sprintf("%a", op(1,x));
     if length(y) > 400000 then
          [Threads:-Seq(Parse(s), s in y)]
     else
          [seq(Parse(s), s in y)]
     end if
end proc:

x:= evalf[1000000](5555/7):

CodeTools:-Usage(F1(x)):

memory used=51.00MiB, alloc change=24.75MiB, cpu time=2.80s, real time=1.04s, gc time=46.88ms

@alshehri 

Yes, just subtract one expression from the other. The y(x) terms cancel, as well as the terms having h^2.

@alshehri 

The h=0 is the expansion point, i.e., it's the Taylor series at or about h=0. The 3 is because I wanted terms upto O(h^3).

@alshehri 

y(x+h):  % = series(%, h=0, 3);

y(x-h):  % = series(%, h=0, 3);

@alshehri 

y(x+h)-y(x-h):  % = series(%, h=0, 3);

Your file did not attach. This is an intermittent bug in MaplePrimes. Please try again.

@landivar Have you tried a simple restart; ?

If that doesn't work, try plotsetup(inline); , then retry the plot3d.

If that doesn't work, try adding the option thickness= 2 to the plot3d. This thickens the gridlines.

If that doesn't work, try adding options style= wireframe, color= black to the plot3d. This should show only the gridlines.

Do you remember which examples you ran?

Or < v > + m, which produces Matrix output.

Another option is v + m[..,1], which produces Vector output.

@Kitonum Yes, your solutions are the same two solutions as produced by my program. My program does not directly prove that these are the only solutions, although it can be easily used to generate such a proof.

Your techniques for the direct solution of such problems are very impressive. Your technique is to step through the entire solution space finding the points that satisfy all the constraints. My technique is to make logical deductions from the constraints and narrow the solution space. As a trivial example, from A = B and B = C, I deduce A = C (where `=` means membership in the same equivalence class rather than simple identity).

My program does this problem in about 0.1 seconds. Your technique takes about 2.9 seconds.

@sunil-maple What format do you want the table? There are 27 matrices in the ring. A 27x27 array with each entry a 2x2 matrix seems to large to put onscreen. So, what format did you have in mind?

Do you mean 2x2 matrices?

@Markiyan Hirnyk Stephen Forrest is saying to select "Factor" from the context menu. This is equivalent to using factor (lowercase f).