@acer 

After I consider after a while, I will write a message or a question.

Please wait until then. Thank you for telling me a lot.

Take care.

taro

@acer 

Thank you for telling me a lot.

Yes. What I want to do is what you wrote: 

int(p(k), k = 0 .. M) = int(alpha - gamma q(k), k = 0 .. M)

And, I want to obtain the result of

 int(p(k), k = 0 .. M) = alpha*M - gamma* int(q(k), k = 0 .. M)

Take care.

taro

@acer 

Sorry. I have an additional question.

What I wanted to do when I asked the question was

integrate both sides of the equation

equ:=equ:=p(k)=alpha-gamma*q(k)

with k, for the range between 0 and M.

Following what the usage of map2 which you kindly taught to me, I did as follows.

g:x->int(x,k=0..M);

equ:=p(k)=alpha-gamma*q(k);

h:=map2(map,g,equ);

Then, an inconvenience occurred. As for the left hand, Maple calculated p(int(k,k=0..M)).

That is, it falsely integrated the argument of p.

Otherwise, I wanted Maple do as int(p(k),k=0..M) on the left hand.

If you have any good idea to do so, please teach me the way to do this.

Thank you in advance.

Taro 

@acer 

Thank you. I couldn't understand that map2 can be used as the way you taught to me, when I first read its help page.

Examples there was, for example,

map2(f, g, {a,b,c});

On the other hand, my equation was y=a+b in the place of {a, b, c}.

So, I think that an equation is like a list with its component being each sides of "=".

Thank you for teaching me the usage of map2.

Take care.

taro

@Kitonum 

Thank you for teaching me the usage of ||.

Take care.

taro

@Carl Love 

When I looked for the meaning of `` in helppage of Maple, that page of ?emptysymbol appeared.

But, I couldn't know what kind of relation that emptysymbol has to the usage of "``", which is used in this question.

@Carl Love 

Thank you Cari Love,

Owing to you, I could understand well about the usage of ``

Then, I could writite the following expression as well.

``(``(-2)*``(-1))/``(``(-5)*``(-1));

On the other hand, I couldn't find the pages of ``, with google and in the help page of my Maple.

If you know some page of it, would you mind telling me about it?

At last, I will repeat thank you to you.

Best wishes.

taro

@ThU 

Thank you for your answer.

I could know why gamma cannot be singled out as a solution.

@Markiyan Hirnyk 

Thank you for telling me how to repeat expand for a few times.

I will get to be able to use the way you showed me.

Best wishes 

taro

@Alejandro Jakubi 

Thank you for telling me about your dividend. I will try to understand its procedure.

Best wishes

taro

@Kitonum 

Thank you very much. I could do what I wanted to do owing to you!

@Adri van der Meer 

Thank you. I could understand what the point was owing to your comment.

taro yamada

@Adri van der Meer 

What I wanted to do is as follows.

Integral is like summation, just the integrand is continuous function of t as q(t).
In this case, I wanted to calculate

u:=integrate(q(i),i=0..M);

diff(u,q(k)), where q(k) is a value of q(i) for the specific i=k.

That is like 

diff(x+y+z,y)

@Adri van der Meer 

 Thank you for your reply. I m sorry to say that you might misunderstand the problem I wrote.

With the calculation you wrote, that is,
v:=Int(q^2,i=0..M)^2;
diff(v,q);
what I obtained was

2*Int(q^2, i = 0 .. M)*Int(2*q, i = 0 .. M)

This is not right, because the answer has to be

2*Int(q^2, i = 0 .. M)*2*q

 q is considered to be a vector with infinite dimension. And, for its particular element q(i), I wanted to differentiate the integral.

 Take care.

 Taro

@J4James 

Hello,

 I wanted to differentiated u with respect to q(i) with the particular i.
The reason I used q(i) not q[i] is that it is necessary for integration.
And, on the other hand, q(i) becomes variable, for a particular i.
I wanted to differentiate u with that q(i).

 Originally, I wanted to calculate this.

 v:=Int(q(i)^2,i=0..M)^2;
 dv:=diff(v,q(i));

which shows an error message.

So, I modified this as

> v:=(Int(q(i)^2,i=0..M)+q[k]^2)^2;
>diff(v,q[k]);

Then, 

4*(Int(q(i)^2, i = 0 .. M)+q[k]^2)*q[k]   (*)

appears. I don't like the expression of (Int(q(i)^2, i = 0 .. M)+q[k]^2) in the (*), and haven't been able to modify this to 4*(Int(q(i)^2, i = 0 .. M). And, with algsubs, q[k] which is in a expression outside of the original expression v, is modified, which is not good for me.

But, I think that my problem might have been settled down owing to you.

Thank you very much.

taro