@Markiyan Hirnyk Is that entrance exam for all students entering the University, or just for those majoring in math?

@SandorSzabo Your file did not attach. This is an intermittent bug in MaplePrimes. Please try again, or post your code as plain text.

@viraghj Sorry, there was one character missing from the worksheet. Thank you for finding and reporting the problem. I've now corrected it in the original Answer. Please try again.

@Carl Love I've made an improvement to the operator &=. Now it can take anything (functions, indexed expressions) on its left side that := can take, and it will be treated the same as := treats it (it doesn't matter if it's already assigned---it will reassign it).

`&=`:= proc(f::uneval, expr::uneval)
local x:= eval(expr);
     print(op(1, subs(_f= nprintf("%a", f), _x= x, proc(_f:= expr=_x) end proc)));
     assign(f, x)
end proc:

@jimb1993 

If you say

Sol:= zip(B, X, Y);

then there are several ways to see the elements of Sol. One way:

interface(rtablesize= 50):  Sol;

The same is true of any Array with a dimension greater than 10.

The second way is to address the elements of Sol individually by indexing: Sol[1], Sol[2], Sol[3], etc.

The third way is to convert it to a list:

convert(Sol, list);

You say that you needed to convert the x and y in B to uppercase. Sorry to say it, but that cannot be true.

Copying from Excel should be no problem.

If your x and y values are in a single matrix A with the x values in the first column and the y values in the second, then you can do this:

Sol:= zip(B, A[..,1], A[..,2]);

@jamesc You just need to change the initial point from 0 to 1. It's positive 1 because I've taken the mirror-image of the function and am looking at the roots on the positive axis, because NextZero only works in the positive direction.

N:= 100:  #Number of roots desired.
Root:= Array(1..N):
#NextZero only works in the positive (forward or rightward) direction.
#We want roots in the negative direction. We need to translate the negative
#roots to the positive axis by using f(-p) and then negating the found root.
Root[1]:= -RootFinding:-NextZero(p-> f(-p), 1):
for n to N-1 do
     Root[n+1]:= -RootFinding:-NextZero(p-> f(-p), -Root[n])
end do;

By the way, that critical point is at exactly p = -0.75.

@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?