## 470 Reputation

8 years, 14 days
Maple is to me difficult. The first version I bought was Maple9, and it was more than 15 years ago. But, I couldn't use it, feeling it too difficult. But, three years ago, I thought Maple might be helpful to my study, and since then, I have continued to learn Maple. As I got able to read the Maple help, I think that I could get to use maple better now than before. But, I feel that I am a beginner yet.

## Surely, but...

@ThU
Surely, in this case, it is easier to rewrite the expression manually.
But, I think I could improve my skill much in using Maple, through asking that question here and reading the code by Kitonum. I owe a lot to people who gave me answers to my questions.

## Thank you...

Thank you. I owe you a lot.
I found from your answer that the basic idea, when a variable overlaps between the part already collected and the part not yet collected, is to replace the part already collected with another variable and to collect the part not yet collected.

And, thank you for showing me the use of freeze and thaw, and how to chooze the already
Thanks a lot.

## Please explain in more detail....

I'm sorry. I couldn't understand what you wrote. What is some subexpression which you wrote? and what can I do if I had defined that subexpression. You posted your
comment while I was modifying what I wrote, that is, in the part of mentioning that algsubs could not be used for appropriately getting the answer. And, if my
remove(has, c1, delta) means your writing that I have to obtain 'that subexpression,'
what can I do after doing it?

## not typesetting...

Thank you for your comment. But, this is not for typesetting, though looking so.
My question is how to do additional collect in the case that the variable with which I want to collect the rest of expression has already been used for another collected part.

More writing to explain my problem, as op([5,2..3],a1) is not -epsilon+z, I cannot use applyop for collecting -epsilon*z + z to
z*(1-epsilon).
On the other hand, I can identify -epsilon*z+z with

But, this identification does not look helpful, as algsubs(d1=collect(d1,z), c1) does not play the role which I expected.

## explanation...

@nidojan

I'm sorry. I think I might have lacked of enough explanation about my question.
What I want to do is to collect the part of -epsilon*z+z in a1 to z*(1-epsilon) in b1.

## I could not use your suggestion well....

I think that your advice is to divide both of numerator and denominator with a specific expression. In that meaning, through doing so, I could simplify the expression which I wanted to simplify. Thank you.

## Thank you...

@Kitonum

Though a similar one, dividing first works well.

e1:=n = (theta-1)*(z-1)*(-k*psi*L*(-(epsilon-1)*psi/epsilon)^epsilon*k^epsilon+K*(-(epsilon-1)*psi*k/epsilon)^epsilon)/(gamma*((theta-1)*(z-1)*(-(epsilon-1)*psi*k/epsilon)^epsilon-(-(epsilon-1)*psi/epsilon)^epsilon*k^epsilon*theta*z*psi));
b:=(-(epsilon-1)*psi*k/epsilon)^epsilon;
c:=simplify(numer(rhs(e1))/b)/simplify(denom(rhs(e1))/b) assuming (k>0);


The problem in this case to me migh have been the use of assuming(k>0).

Thank you.

## Engenvalue...

Doesn't the way to ascertain whether all eigenvalues are positive become an answer?

Vector[row]([r,s]).Matrix([[1,-1/2],[-1/2,1]]).Vector[column]([r,s]);

expand(%)

a:=Matrix([[1,-1/2],[-1/2,1]]);

LinearAlgebra[Eigenvalues](a);

## @Kitonum  In my environment: maple...

In my environment: maple2016, osx EL Capitan, the result of assignment is different from yours. A and B are reverse in my results. Could I ask you to show the way to correct this?

## for example...

I think that what you want to obtain is the limit of g(t) when t goes to infinity.
Setting t=50, the following graph is drawn.

plot(abs(x^(2^(-50))-1),x=-0.1..2);

where it increases between -0.1 and 0, decreases between 0 and 1, and increases above 1.
I think you have to do is to show the part of below where.

By the way, how can I make that graph smooth?

Would you please tell me why "," that is comma, at the last of "evalindets(Expr, 'function', t->op(0, t)), " in yor code,
cannot be replaced with ";" that is semicolon?

## difference between extreme points and cr...

Sorry. As the description of two commands are the same other than the outcome of
examples there, I thought they were the same. But, they are different.
See below.

plot(-(x+2)*(x+1)*(x-1),x=-2.1..2.1);
evalf(ExtremePoints(-(x+2)*(x+1)*(x-1),x=-3..3));
evalf(CriticalPoints(-(x+2)*(x+1)*(x-1),x=-3..3));


The output of ExtremePoints contains the end points x=-3..3, and
that of CriticalPoints does not.
So, in the case of the original question, CriticalPoints, which is Markiyan's answer, is more appropriate.

## To Scot...

I think that I wrote the above anwer after reading mskalsi's question of
"I am interested in derivative. In fact my aim is to extract Maxima and Minima from plot."

As for the extreme points, the following which is  almost the same
as that of Markiyan Hirnyk, just different in the name, is my answer.

f:=0.012981+0.080285*cos(0.9519256799*x)+0.041370*cos(1.903851360*x)+
0.035690*cos(2.855777040*x)+0.000147*cos(3.807702720*x):

Student[Calculus1]:-ExtremePoints(f,x);
I don't know why two commands with the same function exist.
And, as for maximum of f,

Optimization[Maximize](f, x = -6 .. 6);
works.

## I think more details are necessary...

Can you explain the meaning of your A_i B_{i j} = \sum_{i=1}^3 A_i B_{i j} in more detail with some conclete example?
And, please explain the meaning of your second expression of A_{i j} B_{m j} C_{i m} V_k.
From where did ,for example, the expression A_{i j} come from?

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