@Jamie128 

To the side of your question, Physics has the D_ command to compute covariant derivatives (also ThreePlusOne:-D3_) and the ExteriorDerivative command to compute exterior derivatives, besides LieBrackets, LieDerivative and KillingVectors commands, all inter-related. My question is thus only a curiosity: why do you use DifferentialGeometry instead for compute covariant and exterior derivatives?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Entering "EllipticE" should turn ON the typesetting for 1 or 2 arguments. That is fixed within the Maplesoft Physics Updates v.1468 or newer. The not in bold for the two arguments is intentional to distinguish from the one argument case (directly by looking at the function's name), so that is not to be changed.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesofty

The first issue is according to design, as explained by @acer; his suggestion of Physics:-Setup(assumingusesAssume) is the Maple way to make this first example work as you expect using  assuming, without having to set a fixed assumption using assume.

The second issue, the output of D(f^k) assuming k::constant, was a weakness in D, which is fixed in the Maplesoft Physics Updates v.1466 for Maple 2023. As usual, to install it open the GUI and input Physics:-Version(latest);

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi @Carl Love 
Would it be possible for you to show what you say / suggest in a worksheet using 2D so that I can follow? Maybe it is a simple thing to adjust.

Best!

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Interesting ... I understand there is no single approach but different approaches suitable for each person. In my case, I try to see whether my answer's message(s) are clear enough to be understood. If so, only continue in the thread if there is something else (derivable from the original question). Or if the topic changes as soon as I reply, make that explicit in a new reply and only continue in the thread if the new topic really interests me. If the thing extends, or the arguments start repeating, I frequently prefer to quit the conversation - no matter how it looks.

@Jean-Michel 

I adjusted the title according to what you said.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Jean-Michel 
I adjusted the title according to what you said.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

Hi @Jean-Michel
As far as I know, on all platforms, including Windows (several Maple users), the following works fine:

1. Open Maple's GUI
2. Verify the value of libname: be sure you do not have some library interfering in a directory listed when you input libname
3. Input: Physics:-Version(latest);

If that doesn't work for you, item 2. is where I guess your problem could be. People from support@maplesoft.com should also be able to give you a hand if the standard procedure itemized above doesn't work for you for some more elusive reason.

Besides the above, I see in your post "failed to resolve filename C:\Maths\Maple2023\toolbox\2023". The directory where the MapleCloud packages get installed is the one you see entering cat(kernelopts(homedir), "Maple/Toolbox/2023"). So I'd suggest you verify that that directory exists. My understanding is that it suffices for cat(kernelopts(homedir), "Maple") to exist.

Finally, if for some reason that escapes me, the above doesn't help you, I would suggest you manually create the directory cat(kernelopts(homedir), "Maple/Toolbox/2023"), then let me know, and I'll send you a zip with the files you'd need to install in that directory, basically following this structure: 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

This is fixed in the Maplesoft Physics Updates v.1459 or newer. As usual, to install the update open the GUI and input Physics:-Version(latest)

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Jamie128 @Hullzie16 @Rakshak
I misread the original question; sorry for that; I answered again in the same frame where I presented my first answer - see further above.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Without disputing preferences, there is alias:-Show, which handles arbitrarily large algebraic expressions that may (or not) contain subexpressions involving aliased things. For example

There is more; see the output of exports(alias).

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Hullzie16 
I hope you don't take me wrong, but what you are doing is not the proper way of comparing things. I see no bug in Define, nor in series, nor do I see two results; always one and only one:

Download Also_NO_SeriesBug.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

@Hullzie16 

The way you wrote the worksheet, I cannot follow by eye that the steps in sector 1 are equivalent to those in sector 2. But there is a simpler way to compare assuring you are performing the same steps, as shown in this image (mw attached at the end), where you see the two results, where (9) is after Defining the tensor P, and (10) is after taking a=1, b=1 without defining anything, results in the same thing: (9) - (10) = 0.

UPDATE May/1: independent of "no bug that I could see here", in the Maplesoft Physics Updates for Maple 2023, v.1436 or newer, there is a new option for the Define command: computetensordependency = false (default value is true), which skips the most time-consuming verification step. Using this option, the Define(ition) of this tensorial expression of length > 50,000 is performed in ~100 seconds in a two-year-old Mac (M1 chip).

Download NO_BugMaple_(reviewed).mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

@sursumCorda 
That work/comparison is indeed useful. I also see that the number of DEs that Maple can solve and Mathematica cannot is much-much larger than the opposite, both for ODEs and PDEs. I do not work following anything in particular, but yes, this comparison is a good guideline for improvements; to increase the existing Maple advantage in this area.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Diasaur 

Download noncommutative_prefixes_and_quantum_operators.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft