@Michael_Watson 
I am receiving "404 - File or directory not found.", maybe a problem in Mapleprimes server? Can you retrieve it?

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

@Alejandro Jakubi 

Unfortunately, it sometimes happens that images of equations, that are there when I post, get lost afterwards. The input was like dchange(n = m-1, Sum(f[n],n=a..b)). Regarding renaming PDEtools:-dchange into something else: yes, it would makes sense. I added this functionality for "changing variables in general" in PDEtools in 1997. Actually there are a couple of things in PDEtools that would be more useful if they were more visible, among them: PDEtools:-<Solve, casesplit, declare>. Perhaps if there is some spare time this could be done. At this point anyway I am sufficiently happy with having all this functionality in the system.

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

@bao 

Rules can be set for Commutator and AntiCommutator of objects, that typically are not commutative. That does not prevent you to set a rule for a couple of commutative objects indicating it as an AntiCommutator rule, you know, where, when A and B commute, AntiCommutator(A, B) = 2 AB, so multiply by 2 both sides of the equation you show and replace the left-hand side by  AntiCommutator(A[i], A[j]); there is also more than one way to do this, depending on whether you define A and/or Q as tensors, which mainly tells the system that it should (or not) use Einstein's sum rule for repeated indices.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Carl Love 
Hi Carl, yes, you are correct, the whole issue here is in expand/Sum, that is not doing the expansion, and then for some historical reason got coded in the wrong place as IntegrationTools:-Expand. See for instance the reverse operation, combine: we have the sum and int cases coded together there. It is easy to fix expand/Sum anyway (but for the time-available issue, you know ...). I will give this a look and post a fix in the Maplesoft R&D DEs and Mathematical Functions webpage hopefully this week, together with some other recent developments in the FunctionAdvisor.

But this expand/Sum issue deviated the focus from the main issue: the general command for changing variables in Maple, in everything (not just integrals, nor just sums, nor just limits, nor just derivatives, etc.) is in fact PDEtools:-dchange.

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

@Carl Love 
Note that IntegrationTools:-Change is just a wrapper around PDEtools:-dchange. Also, you see you do the Expand step separated, subbing Sum = Int. It shouldn't be that way. expand(A) should work. fixing expand/Sum will also make this work within PDEtools:-dchange passing the optional argument expand (dchange accepts a simplifier - it is explained in the help page).

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

@Carl Love 

Hi Carl, the context for my comment is the last example of the help page for dchange. Take then (17) from that help page and try solving for s using solve and PDEtools:-Solve:

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

@John Fredsted 

It is mentioned in the Updates page: the final update for Maple 17 is Physics-61.1.mla.zip. That happened March 19, after the release of Maple 18. So the fix to the issue you posted is in the update for Maple 18, not for Maple 17. Note that maintaining updates retroactively, for previous releases, is difficult, because not just Physics but the whole library is changing, and Physics depends on these changes; in this case many things changed from Maple 17 to Maple 18. Independent of that, on return I will see if I can prepare a personal fix for you regarding this particular issue. 

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@jakubi 
Indeed, for Maple 16 a complete set of General Relativity tensors got added to Physics, mainly D_, representing the covariant derivative, Christoffel, LeviCivita in curvilinear coordinates etc. With these new commands it is sort of straightforward to tackle tensor calculus problems as the ones mentioned in this post. I show how to do that for the divergence of a stress tensor in polar cylindrical coordinates in an answer appearing further below (or further above ... I never know where is the answer appearing :) )

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

@John Fredsted 

You have a point, and yours is in fact the third MaplePrimes post that asks for the same, a sort of manual for Physics. It is not that command-documentation is missing, I think, but that the amount, and kind, of functionality available is beyond what you can explain in useful ways within traditional help pages for commands.

To fill the gap at some point I added the page ?Physics,Examples, with sections "per area". That is a different concept than "per command". It did help well. Then I added Physics,Conventions, to have all the conventions in one single place - that also helped.

By now however ?Physics,Examples is too large for a single page, even if its approach is still valid, I think, and the conventions would also benefit of a splitting by physics area. The way to go is to add material to fill the gaps in these two pages and organize the whole thing into a mini-manual for Physics, say as an alive computer algebra document, about Vector Analysis, Mechanics, Electrodynamics, Quantum Mechanics, etc. (most of the current sections you see today on ?Physics,Examples and some more), where you could rapidly find computations of the kind that you need to develop. For this manual to be useful it needs to be really very short and with very good examples more than anything else.

I will think about and see how to move this project ahead during this year.

Regarding what you have for documentation today, the help pages ?Physics,Examples, ?Physics,Conventions and ?Updates,MapleXX,Physics, where XX is 16 or 17, plus of course the help pages for the commands themselves, do tell most of the story, even if in fragmentary manner.

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

@juggler 

I personally prefer overwriting the system library folder, because the new library is indeed an updated version, so why would one want to use the old one, but if you want to have both options then installing in a personal directory is the way to go. Or also a third alternative: rename, in the system library folder, Physics.mla to Physics.mla.old, then put the udpated Physics.mla in that directory. In that way you can also go back to the original M17 library if you want by deleting the updated one and renaming back Physics.mla.old -> Physics.mla.

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

@rashmi 

I suggest you to give values to e and l and use dsolve/numeric and odeplot (see ?dsolve,numeric and ?odeplot). Sometimes of use too, you can combine plots for different values of [e, l] using plots:-display.

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

@juggler 

No, there are no limitations, as far as I can tell .. but I am not the appropriate person to answer this type of question - perhaps people at support@maplesoft.com can give you a more exact answer.

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

@Mac Dude 

All ok, just one thing: when testing your example with currrent Maple (17), remember to update Physics with the latest version found at the Maplesoft Physics: Research & Development webpage, where you get not only new developments but also bug fixes to the problems reported.

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

@John Fredsted 

Hi, yes, for sure. I'll post again here, in this thread.

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

@Alejandro Jakubi 

Not sure what you mean. In Physics you can set the metric to whatever you want, including arbitrary. The same in DifferentialGeometry. But it is current Maple, not Maple 12.

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