@Carl Love   I do not understand why we need to override the matrices. Maple tests  A  and  A1  as the identical matrices:

restart;

with(LinearAlgebra):

A := Matrix([[1, 2, 3], [3, 1, 2], [2, 3, 1]]);

A1 := Matrix(3, shape = Circulant[[1, 2, 3]]);

Equal(A, A1);

@Muhammad Usman   

applyrule(exp(x::anything)^y::anything=exp(x*y), expand(exp(2*a+b)));

@Markiyan Hirnyk   I do not know the causes of your problems. Here's a screenshot of the playing this animation in Power Point. Below is visible panel to control animation:

@Markiyan Hirnyk   I do not understand what's the problem? Click on the picture  and the bottom panel appears to start the animation.

Here is a sample ppt-file with the animation of the tangent line as the limiting position of the secant. Animation is made in Maple (M 12 classic), saved as a gif-file and inserted to Power Point in the above method.

Animation_tangent_line.pptx

@Markiyan Hirnyk   Everything works, I checked. On the instrument panel of PP click insert  (not paste)  and so on (see the order of actions above). After  All Files  click your  gif-file from documents.

@laporte bernard   I do not see any errors. To better see the elliptic paraboloid, you just need to extend the domain of definition for the graph of the function  f (x, y)  (the red line on the surface shows the steepest increase of the function  f(x,y) ):

restart;

f:=(x,y)->2+x^2 +1/4*(y^2);

Px, Py:=1, 2;

DPx, DPy:=D[1](f)(Px,Py), D[2](f)(Px,Py);  # Partial derivatives

maximize(DPx*cos(alpha)+DPy*sin(alpha), location);  # Maximum of directional derivative

A:=plot3d(f(x,y), x=-3..3, y=-sqrt(36-4*x^2)..sqrt(36-4*x^2), axes=normal):

B:=plots[arrow]([Px,Py,0],[DPx,DPy,0], color=red):

C1:=plots[spacecurve]( [1,2,t], t=0..4, color=black,linestyle=2):

C2:=plots[spacecurve]( [2*t+1,t+2,f(2*t+1,t+2)], t=0..0.8, color=red, thickness=3):

T:=plots[textplot3d]([[1,2.2,0,"P"], [1,2.2,4,"Q"]], align=right, font=[TIMES,BOLD,16], color=blue):

plots[display](A,B,C1,C2,T, orientation=[-15,65], scaling=constrained);

@Markiyan Hirnyk   Thanks for the clarification of the causes of issues.

@acer  Thanks for the detailed answer! 

@Kitonum  If you replace the fourth line of code with the following line, the procedure will run faster:

L:=[seq(ithprime(k) $ min(n, floor(a/ithprime(k))), k=1..pi(a))];

@fairuzalwani 

E := [0, 2, 7, 15, 26, 40]:

map(C, [3, 10, 24], [0, 2, 7, 15, 26, 40]);

                           [3, 4, 5]

@Carl Love   

E:= [0,2,7,15,26,40]:

1+ListTools:-BinaryPlace(E, Pi);

   Error, (in ListTools:-BinaryPlace) the 2nd argument should be of type {numeric, string}

@one_man   a := remove(i -> i=x+2, a);

@Markiyan Hirnyk   For earlier versions of Maple yours is not appropriate. For example in M 12

seq(RandomTools[Generate](float(range=-1..1, digits=5, method=uniform)), n=1..20);

       Error, (in RandomTools:-Generate) cannot specify a range crossing the origin

So I'm trying to write a version-independent code.

@mahmood180  Yes, I already wrote to you about it.