As I am new to using the statistics package, I have some doubts about how to perform certain operations in Maple.

For example, let sigma be a variable containing any real number, finding the average is easy, just use the command A0:=Median(sigma) and if you want A (see image below) just take A1:=A0^2. However, the terms that make up <sigma^2> cause a certain difficulty, how to do this? In other words, calculate the B of the image?

sigma := [2, 4, 0, 6]

AMedia := (2 + 4 + 0 + 6)/4;
AMedia1 := AMedia^2;

A0 := Median(sigma)

A1 := A0^2

BMedia := (2^2 + 4^2 + 0^2 + 6^2)/4

sigma0 := sigma^2

sigma1 := Mean(sigma0)

.......................................................................................

I need to highlight all terms that contain eta, my variable, for example (A0)+(A1)*1/eta+(A2)*1/eta^2+...(An)**1/eta^n and so on in my expression call from P. However, when I select eta through the collect command, maple is unable to carry out the command.

P := expand((cosh(k*eta) + alpha*m*sinh(k*eta)/eta)^3);
P := convert(P, exp);
P := expand(P);
P := collect(P, eta);
P := combine(P);

Once these have are in evidence I need to select the coefficients A0, A1, A2, etc. How to proceed if eta are in the denominator and maple does not work with this possibility? This it'was my tentative

B0 := subs(eta = 0, P);

B1 := coeff(P, eta)

B2 := coeff(P, eta^2)

I actually tested the possibility of  1/eta instead of  eta and it didn't work

Anteriorly, I had done a question that you answered in the forum and it basically it was about the simplification of a equation. I'm posting the print of the screen and the code because the question of today is similarly, but not completely, because there are something that make more complicate the code that I devolved.

restart;
Hi := -Delta*S1^2 - J*S1*S2;
R1 := S1*exp(-beta*Hi);
R1 := add(R1, S1 = [--1, 0, 1]);
R2 := exp(-beta*Hi);
R2 := add(R2, S1 = [-1, 0, 1]);
S := R1/R2;
S := convert(S, trig, {J*S2});
S := simplify(S);
S := convert(S, exp, {Delta});

In this case I had to put in evidence the therm exp(Delta beta), where I simplified the expression. Now, we have more 2 variables (+2 and -2) to substitute in the equation. The code is:

restart;
Hi := -Delta*S1^2 - J*S1*S2;
R1 := S1*exp(-beta*Hi);
R1 := add(R1, S1 = [-2, -1, 0, 1, 2]);
R2 := exp(-beta*Hi);
R2 := add(R2, S1 = [-2, -1, 0, 1, -2]);
S := R1/R2;
S := convert(S, trig, {J*S2});
S := simplify(S);
S := convert(S, exp, {Delta});

In the last line we had the final equation

What should I change in the code for that my exponential function continue in evidence? This is, for my expression  be

(4*sinh(2*J*S2*beta) + 2*sinh(J*S2*beta)*exp(-3*Delta*beta))/(2*cosh(2*J*S2*beta) + 2*cosh(J*S2*beta)*exp(-3*Delta*beta) + exp(-4*Delta*beta))

In the system below, I need to solve the solution algebraically (it is known in advance that from "V3" that a0=1,just open the V3 command).

V := exp(lambda*S) = S^4*a4 + S^3*a3 + S^2*a2 + S*a1 + a0;
V1 := subs(S = 2, V);
V2 := subs(S = 1, V);
V3 := subs(S = 0, V);
V4 := subs(S = -1, V);
V5 := subs(S = -2, V);
fsolve(subs(a0 = 1, {V1, V2, V4, V5}), {a1, a2, a3, a4});

I already know the answers, but I need maple to provide me with the command in the form

a1:=(1/6)*[8*sinh(lambda)-sinh(2*lambda)] and

a2:=(1/12)*[16*cosh(lambda)-cosh(2*lambda)-15],

a3:= ... etc.

What is the best way to do this?

Once the terms have been selected, as below

I only need to keep terms that contain a certain function with generic arguments, for example, tanh(x), in this case, that is, I want from A01

-(m2/4) tanh(2k-2ç)+(m2/16) tanh(4k+2ç)+-(m2/4) tanh(2k+2ç)+(3m2/8) tanh(2ç)

and delete the terms

3/16-(3/16)m2^2

What's the best command to make that? In other words, always exclude terms that do not accompany tanh