@Markiyan Hirnyk I agree with you 100% about what is the technically correct definition of function in Maple. However, I believe that the Asker was asking about how the terms are used in actual practice.

Mac Dude: Did you see this Answer? Did it help? Why no reply?

What output do you want in each of the cases? Would it help if you eliminated the constant term (constant wrt x0) before calling coeffs?

@Alejandro Jakubi I also have not received a single email since the update.

Markiyan: Have you received emails since the update, on Thursday I believe?

@Markiyan Hirnyk I would call it a command, but I don't think that that usage is universal. It's certainly not a function.

@Bendesarts Stop using evalm!

Matrix multiplication is done with . not with &*

Pi is spelled with capital P: Pi not pi.

Can you please provide the exact text of the problem that you are working on? I don't think anyone is going to be able to help using only the information that you gave above.

@Bendesarts I have not been able to download your latest version of the file. There are still bugs in the MaplePrimes software. I am not sure that this will be posted either. I don't think that they are working on the bugs over the weekend. It may be Monday before it works.

You are confusing a procedure's definition with its invocation or execution. The lines that begin

AA:= proc(S,t)
local ....

are the procedure definition, while AA(Sol, t) is the invocation. The relative order of the definition and the dsolve makes no difference, but both must occur before the invocation. It is only the invocation that creates the Matrix.

@wzelik The file is accessible now. The 404 error was due to a bug in the MaplePrimes software.

@Bryon The list "All Recent Posts and Questions" is currently ordered reverse chronological by the time the Post or Question was created. It used to be reverse chronological by the time of the last action. "Action" used to be defined as an Answer to a Question or a Comment to a Post; Replies to Answers did not count. I would prefer if Replies to Answers were counted as Action.

I have not received a single piece of notification email from MaplePrimes since you made the update two days ago. There has definitely been activity in threads (like this one) that I participated in which ordinarily would have generated email. The "subscribe to" box has been checked on all my posts.

@Bendesarts Again, I can't download the file. Undoubtably this has something to do with the MaplePrimes update.

@Axel Vogt That last-mentioned bug seems to be intermittent. I wonder if it happens when another reply in the thread it being editted at the same time.

Yes, the matrix inverses are too complicated to do symbolically. So, I suppose that you have a differential system which you will solve for the ten functions alpha(t), beta(t), psi[1..4](t), and phi[1..4](t), right? And for that you are going to use dsolve(..., numeric), right?

So, we can consider your complicated expression as a matrix-valued function of t, right? And you only need it evaluated for numeric values of t, right?

If the answer to these questions is "yes", then it will be possible to modify your code so that it very quickly evaluates the matrix expression for any numeric t, although I have some mild concerns about numeric stability.

@Bendesarts I can download the file now. The problem was due to a bug in the recent MaplePrimes software update. You did not do anything wrong. Sorry for the confusion and hassle.

@gkokovidis Yes, I have noticed that pages load significantly faster. I was addressing specifically the issue of the speed with which updates appear in the right sidebar column: "Active Conversations", "Recent Posts", etc. I have not noticed an improvement in that. Indeed, there was a Question from two days ago that I answered 8 hours ago which still has not re-appeared in "Active Conversations".

I was able to login after deleting my MaplePrimes cookies.

A new bug I just encountered: While editing this Comment, I pressed Submit. The page refreshes, but it doesn't take me out of the editor. But the edited version is posted anyway.