I think that it would be nice if there were links to some maplesoft pages relating to mapleprimes, in the top page of mapleprimes; such as the pages of programmes of maplesoft, and twitter of mapleprimes and a facebook page, if there is, of maplesoft.

@Sotto
The cause of the error seems to me that the same character P, in P:= in the procedure, and, in it of P[1] or P[2] is used.
If you change P in P:= brabra to q:= brabra, error does not occur.

Ps:=proc(f,g)
local q;
q:=simplify(diff(f,P[1])*diff(g,X)-diff(f,X)*diff(g,P[1])+
diff(f,P[2])*diff(g,Y)-diff(f,Y)*diff(g,P[2]));
end;

Assigned variable q:= is regarded as  a local variable by maple, so
you don't need it as pointed out by Mr. John Fredsted, while in my
environment a caution message telling me I don't specify q as local appears. 

As for the reason why P in P:= and P in P[1] should not be the same character P, I don't know.

@John Fredsted
@Carl Love 

Thank you very much.
I owe all of you a lot. I will write later after I understand your codes.
But, your codes work well.

If I've gotten to be better in using Maple, it is due to people's, especially Carl's teaching it to me here, other than maple support's effort to answer to my questions. And, I'm sorry for rude writing in my reply
in the question in the orders of factors.

taro

@Bryon
Thank you for your effort to improve the use of mapleprimes.
I hope spams will hardly be seen.
 

Thank you. Joe Riel,

Your post of frontend is very helpful to me to understand what
front end does.
taro
 

@John Fredsted 

Thank you for telling me the way to use remove and select in an actual 
situation. I could learn a lot from your code.

@Kitonum 

Thank you for your answer.
Especially, thank you for having me notice that the form of omega^(sigma-1)*L, that is the form `^`  accompanied with `*`
cannot be substituted, but thinking of separating them, that is
omega^(sigma-1) and L, problems such as subs can be solved. 
Especially, in your second way using subs, this appears apparently.
That is, subs(omega^(-sigma+1)*tau*L=t, rhs(aa));
doesn't work, but your code works.

And, I'm sorry for not noticing what you were trying to tell to me.

@Joe Riel
Thank you very much. Owing to you, my code becomes shorter.
And, I'm sorry that I didn't notice that your code is perfect,
with me not noticing where to put factor.
lhs(aa) = frontend(collect, [rhs(aa), omega^(-sigma+1),factor]);
And, your explanation of frontend in the post was very helpful to me.
http://www.mapleprimes.com/posts/41944-Frontend
 

@Carl Love 

Thank you for your reply, and thank you for the reason why changing orders occurs.
In my case, sort removes changing orders so far.
But, if I opened the second worksheet with a new kernel, orders change.
So that, I had to take care to open the second one with the same kernel which I used for the first worksheet and for which kernel I used for the 
first worksheet, I can find at the foot of the first worksheet.

taro
 

@Mac Dude 

Owing to you, I got to use a package, making it.
it saves space of a worksheet a lot.
And, I use "save" command like this to have a file of names of equations:

#save a1, a3, a4, a6, e2, e3, a4, e3_1, e3_2b,e8_3_2, e1_5, #ea_0, e5, e6_1, e7_7, e3_7,
#e8_3_2, e10_1, e11_9, e12_4, "test.mpl"

And, in a new worksheet, I read that test.mpl with the code of
read("test.mpl");
This way is quate a lot of saving of space and time.
 

taro

@Carl Love 

I could know that inserting sort(%) before using applyop puts the
expression in the order which does not change each time I clicked !!!, even if restart was written at the start of a worksheet.

taro

@Carl Love 

Thank you for your reply.
Surely, simplify brings the same result as through my code, as "k" can be ommited between the numerator and denominator in this case,
which I noticed now reading your comment.

In this case, simplify is useful, but in other case, if the order is unreliable
to depend on the order of factors, what kind of ways are there which can be alternatives to the way depending on the order?

taro

@tomleslie 

Thank you for your answer.
I'm sorry that the file I appended is not appropriate one enabling
that error I wrote here to be reproduced. I removed "restart" in the  beginning of my original code. Then, the phenomena that form of
equation changes each time I clicked !!!. dissapeared, but once I
entered "restart" and clicked !!!, error continues to appear even if I
removed "restart" and cliked !!!, until I close the worksheet and I open the worksheet again.

Best wishes.

taro

@acer 

Green-arrow uploard doesn't work in my circumstances as well.
In 3. Insert Links Or Content, insert link bottun does not respond to
the click on it. I am using macosx 10.11.6 and maple2016.

taro

@Christian Wolinski 
@Carl Love 

Thank you for teaching me the code, and for using the use of ",".

Best wishes.

taro