Hi @Carl Love 

Download disambiguating_parenthesis.mw

@segfault 

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

Download Relative_sign_of_the_Lagrangian.mw

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

@Jamie128 
Yes. It is possible to use Physics:-LagranteEquations to get field equations for gravity by using a (modified gravity) Lagrangian. Check the attached version of the help page of LagrangeEquations - it is reproducible by installing the latest Physics Updates (open Maple and input Physics:-Version(latest)).

Download LagrangeEquations_PhysicsUpdates.mw

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

@nm 

A dot release is not a version ahead. You need to be clear about this. Only a few bug fixes enter the dot releases, fixes considered critical for one reason or another. The Physics Updates contain significantly more fixes than that, also developments (entirely absent from dot releases). So no, you do not have Maple 2 versions ahead.

About your comment regarding "... fixes for very old bugs", what is what you consider old? The fixes mentioned in this conversation are for bugs all of them newer than March 2024, this year.

Your statement about odetest hanging does not change what I said before. In that "odetest hangs" post of yours, first, you show it does not hang. Then you show that if you first interrupt computations using timelimit and assumptions, next a hang occurrs. Perhaps you are unaware that interrupting a computation in that way leaves fragments of results in caches. That does not usually generate problems, but sometimes it does. In particular, your problem in that post involves is, assume and coulditbe. As you probably remember, in some cases, is and coulditbe interrupt with an error the first time, then they do not. These nuances can produce problems as the one you mentioned, not a problem in odetest.

By the way, if you want to know what hangs, Maple offers the tracelast instruction - I already mentioned this to you before. That allows you to post the actual problem, which in your example is not a problem in odetest; if it were, then it would have hanged the first time. It is also not a problem in the Maplesoft Physics Updates, even if its presence uncovers a problem not noticed before - that sometimes happens, you know that too.

Then the way you wrote this post I am commenting, it does look like "why are the fixes found in the Physics Updates not present when I remove the Physics Updates?" For me, that indicates you are not clear about how this works. Maybe you were not clear of what a dot release is.

Anyway, I can see you expecting even more from the software; I don't share your expectation, the comments aim at explaining that.

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

The Maplesoft Physics Updates is a project that aims at bringing to the current Maple release fixes that are present in the version under development, as well as new developments in the areas of Physics, Differential Equations and Mathematical Functions. Somehow, your posts these days, @nm , either indicate you are not clear about that or perhaps you are trying to say something else?

In this one above, you say that a version of the Maplesoft Physics Updates fixed a reported problem (and, you know, also other problems not reported in Mapleprimes). Well, if you remove the Maplesoft Physics Updates, the problems that it fixes are not fixed anymore. I find that natural—what were you expecting?

I also mentioned other times that installing the Physics Updates may reveal a problem that was not apparent without it. Yes, that can happen—report the case. Depending on the problem, it may get fixed in one of the next versions of the Updates, or you may need to wait until the next release because, sometimes, other problems are seen as a higher priority. All this is known.

In summary, you have two options: install this Maplesoft Physics Updates package and have all those fixes and developments "in advance", or wait for them until the next Maple dot or full release (for Maple 2024, that would be next year).

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

@Hullzie16 
Nice reply. Attached are a few comments intercalated in your worksheet that may be of interest. Physics is an environment with a myriad of simplifications for the input. They are not necessary but make entering things easier.

Tensor_Respond_(comments).mw

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

This ODE system is solvable with the existing dsolve. But there is a problem in simplify subroutines. Before calling dsolve, input debug(`simplify/RootOf`, statements = false, depth = 1) and you see, at the end, the line that causes `simplify/RootOf` to interrupt with the Error message you saw. It shouldn't happen. I will see to include a fix for this in the next or so version of Maplesoft Physics Updates for Maple 2024, and write again here.

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

@mehran rajabi 
In that case you can use PDEtools:-dcoeffs. What confused me and I imagine others is that in your question you said "[Given the equation] ... I want to calculate separately, c1,c2,c3,c4,c5" (in a computer algebra context, that has the meaning of performing some calculation) while, actually, you do not want to calculate anything, only extract the coefficients.

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

Hi @Carl Love, there are various, perhaps more like "many", things about the ODE and PDE code, the FunctionAdvisor, conversion network for math funcs, Physics ... that, while documented, the details are so many that end up buried, not noticed. The syntax you refer is explained in ?dsolve,system; scan for 'ranking', it appears almost on top of the page and also is explained in its own subsection, "The unknowns of the problem and rankings".

My impression of this thread is that the question was not properly formulated, or I may have understood it wrongly ... - I was in doubt. Mainly: my interpretation of the question is that this was about solving a system with f(x) and 5 c(x) "functions"whose derivatives are equal to 0, and the solution desired involved "f as a function of the c, and the c as functions of themselves at most", and that is what this ranking represents.

So, if I am correct, what was missing was a more precise description of what was intended. After that, the formulation followed naturally (for whoever knows the functionality available in 'ranking' details).

Best

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

@nm 
Thank you. I added as a PS the worksheet containing the tracelast output, which is what allowed for reproducing the problem and fix it. And thanks to @aroche for his quick fix. The fix is already uploaded in the latest Maplesoft Physics Updates for Maple 2024, so to activate the fix, as usual, open Maple and input Physics:-Version(latest).

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

@nm 

Generally speaking, the more extensive is your post, the most unreadable and time-consuming. I suggest you to try to make your reports more compact. By the way, I work with GUI. Always try GUI first. If I cannot reproduce I move into 1D Math input, then TTY.

Now on the issue: there is a bug in the subroutines of `simplify/common/factors`. I passed the problem to the person who wrote the routine, I suppose we will have a fix probably by the end of tomorrow or Friday. Regarding your comments about whether you display or not things ... I don't know. The bug - restricted to the input to the mentioned routine, however, is reproducible no matter what you display.

Best

Thanks Austin, for the so quick fix; it is uploaded now within the Maplesoft Physics Updates v.1793. To install: open Maple and enter Physics:-Version(latest)

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

@C_R 
It is too time-consuming to answer about the details, but here are more comments. I think your approach, "based on observations", is the right approach, always. The page ?dsolve,setup is relevant only for those who want to have a glimpse on how dsolve is coded, its logic, and perhaps change the way it works. It is not a page of interest for many people. Its existence, perhaps, is more related to my academic origin/teaching: do not present black boxes, and never fall for "I know better". For the same rasons you have the PDEtools:-Library and its help page. Regarding the formulation known as d'Alembert's method, this method is present there, under `dsolve/methods`[1, high_degree]. The page on dsolve's setup could perhaps say "everything starting with 1 in eq.(1) of the page is about methods for 1st order ODEs".

Regarding PDEtools: I wrote this package before moving to Canada, then immersed myself into coding a new ODE solver and the symmetry methods for ODEs, followed by extending PDEtools with symmetry methods for PDEs, finally rewriting the DifferentialAlgebra package. I suppose that due to this historical sequence these two packages PDEtools and ODEtools (this one exists only on background, invisible) are strongly intertwined, and connected with the three differential elimination packages mentioned in PDEtools:-casesplit.

In the end, once you realize that from a solving-logic point of view all these things are differential equations of different orders and number of independent variables, the distinction between ODEs and PDEs (or even non-differential equations) is of little relevance: the majority of the tools for PDEs are of use for ODEs. And some commands are indeed present in both DEtools (the visible package for ODEs, not PDEs) and PDEtools, like casesplit, dpolyform, diff_table, dsubs, ... More important: the subroutines presented in ?PDEtools,Library, are used all around in the ODE code.

Regarding your last question, there is a help page, ?dsolve,education, that presents most things, though indeed not an example as the one discussed in this post (branches and related stuff). It may be good to add such an example. Still, the documentation for differential equations is already so large and detailed that adding more may help in some way but, on the other hand, adds clutter. In part, for that reason, I wrote the odeadvisor and its help pages together with dsolve - trying to provide a more structured way to peek at what dsolve does. Anyway, I will think about one more example.

Finally, I share your impression that "studying ODEs with a textbook" does not make sense. In my case, I learned about symmetry methods to then discover the standard classifications shown in textbooks (mainly Kamke's and Zwillinger's) and note that they were only a minimal subset of particular cases of symmetries or integrating factors.

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

@vv 
Yes. It is adjusted in v.1786 of the Physics Updates.