@srmaple 
The system is nonlinear, so the ordering you choose to decouple it frequently results in different forms of the solution. If you do not indicate any ordering of the solving variables, dsolve will choose for you. You indicate that ordering by passing the unknowns as a list, as @nm has done above. Answering your question, I'd suggest you try the two orderings and see which one results in a solution closer to what you expect. I'd also suggest you to take a look at the help page ?dsolve,system

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

@nm 
Unlike Mathematica, in Maple, when you enter simplify(A), you simplify everything, including a last pass of the result through simplify/size, while a call of the form simplify(A, size) only attempts the simple size manipulations explained in its help page, and simplify/size is pretty good at that.

So, no, your comparison is fallacious and does not have the meaning you imagine it has, because simplify(A) does call simplify(..., size) after simplifying everything else. That said, I agree with @acer. Recent developments in simplify make the result by simplify that you posted originally look more like a bogus thing. It is tracked. I will probably include a fix in one of the following Physics Updates.

Besides the above, where did you get the idea that Mma:-LeafCount is the oracle? Check this more meaningful comparison, including the output of Mma:-LeafCount:

Download simplify_size.mw

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

@Kevin Dragnet 
There is a large number of adjustments (~700) in the Physics package of Maple 2024, and several new developments (e.g. DiracConjugate). But the most impactful developments, related to the ability to compute Equations of Movement (actually Field Equations) directly from a Lagrangian, and for computing with spinors without having to represent them with all the spinor indices explicit, were both unfinished. We decided not to present them until then. 

Among other things already visible in the released version (albeit not advertised), concerning General Relativity (GR), the LagrangeEquations command can now compute Einstein's equations from a Lagrangian (density) that depends on first and second order non-covariant derivatives of the metric (the typical situation, e.g. through the Ricci trace); Fundiff has its functionality extended to handle the tensors of GR without having to rewrite them in different ways; diff, Substitute and SortProducts received extensive reviews and enhancements; there is a new concept: D-tensorial derivatives, that allows for representing derivatives of abstract functions of tensorial arguments, as we see in standard textbooks. And perhaps the most important improvements happened in the Physics:-Simplify command regarding tensorial expressions, for example involving non-covariant derivatives in curved spacetimes, a difficult problem that is key in GR. The Physics:-Vectors package also received improvements.

Overall, the case is that we attempted a big jump in functionality in Physics, a breakthrough but it was impossible to do it in one single development cycle. We are targeting completing them for Maple 2024.1.

Meanwhile, these new developments in Physics are entering the Maplesoft Physics Updates (together with posts to appear here in Mapleprimes) as soon as they are ready, from where anyone with Maple 2024.0 will be able to start working with them. I will prepare the first version of these Updates for Maple 2024 tomorrow, including some of these new developments, and intend to do a post regarding the automatic computation of Einstein's equations from a Lagrangian density next week.

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

@Hullzie16 
Nice response. Note also that Physics includes an option, cosmologicalconstant that you can set using Setup. This is a copy and paste from the help page for Physics:-Setup:

• cosmologicalconstant = 
    "0 or any algebraic expression."
  The default value for the cosmological constant is 0, so the Einstein and EnergyMomentum tensors are proportional. You can set the value of this constant to any valid algebraic expression, in which case the relationship defining those two tensors includes an additional term with this constant as usual - try for instance entering Einstein[definition] or EnergyMomentum[definition].
  ​​​​​​​

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

I don't understand yout question. Could you clarify what you mean by "a complex conjugate such as z" which is not conjugate(z)? 

Note also that when loading the Physics package, you can compute with z and conjugate(z) on equal footing, see this MaplePrimes post about Wirtinger derivatives.

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

The function-parameter k is referred as ".. the modulus k entering the definition of the Elliptic, JacobiPQ and InverseJacobiPQ .. " after formula (6) of help(EllipticF). That said, I agree it is clearer to call k 'the modulus' right away to avoid a potential superficial reading confusing it with '.. a parameter m = k^2 ..'. I adjusted the help page accordingly, following your suggestion.

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

@Thomas Richard 

It is not a correction of the latex of previous Maple versions but a completely new, from-scratch, latex, that includes File > Export > LaTeX, and Copy > as LaTeX.

This new latex command is free of all those problems like the one mentioned in this question.

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

@acer, @Carl Love, @rlopez, @C_R

This is now implemented and the change distributed within the Maplesoft Physics Updates v.1482 or newer, for everybody using Maple 2023. As usual, to install, open the GUI and input Physics:-Version(latest).

The solution implemented is at library level, therefore you need to install the Updates. The problem, however, is actually a GUI issue, and is being investigated as such, probably to appear fixed in the GUI directly in the next Maple release or so.

By the way: I noticed approx 100 differences in our test suite, all of them showing a better display now, the improvement hits across the board. Good catch Robert!

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

@Carl Love 
Instead of subs("&uminus0;" = "–", ...) input subs("&uminus0;" = ("–", "fontweight" = "bold"), ...) and you see the difference. Regarding the other two things you mentioned, vertical position and extra very thing space, none is addressable in a simple way, but anyway, I think those are not the main issues.

If we are all on the same page, I will take a look at what happen with the existing typesetting tests and implement the change. Then distribute it within the Maplesoft Physics Updates as usual so that anybody using Maple 2023 can have this improvement.

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

@rlopez 
ndash or uminus0 are just typesetting tokens, about "how it looks". What is behind, so "what it is", is always the same thing, -1, or -x, etc.

So, is ndash preferred to the current (which is uminus0)? In both a number and a letter?

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

@acer, @Carl Love, @rlopez, @C_R

Download: unary_minus_typesetting.mw

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

@Jamie128 
Indeed, the Physics package is not for working with differential forms (a case where you'd need a wedge product operator). For that, you either have difforms (perhaps more abstract) or DifferentialGeometry (I am co-author of DifferentialGeometry).

Still, as said, covariant and exterior derivative commands are part of the Physics package, and since you mentioned those .. By the way, since Physics implements calculus with anticommutative variables, and the product operator knows about them, including differential operators as part of a product, it is possible to formulate things that you'd typically formulate with differential forms alternatively to tensorial representations.

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

@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