@Sergio Parreiras 

Yes, you can specify both the ordering for the dependent variables, and independent of that also for the independent variables. All this is explained in ?PDEtools,casesplit, give a look please at the section "Optional Arguments". Indeed these are the two options that can make a relevant difference, also the number of rounds; the 'ctl' together with the 'casesplot' options may also server to identify what is the branch that is not terminating, making the whole process hang, and in that way you may be able to get results for the terminating branches (ctl carefully timelimit the non-terminating ones) and then consider any more special strategy for the non-terminating ones.

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

@ Kevin

Great that it works well for you. Kevin, trying to do (say step by step) the computations that an existing command can do (as in 'all in one step') is an interesting exercise, and frequently tells about functionality missing, or things not working as expected, here and there. Please post these. We will give them a look. Most of the enhancements of the last year are related to people's feedback. Other times you will find that things do work as expected, and posting the example (now as a post instead of as a question) is also interesting - it helps everybody understand different ways of verifying or performing computations.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Carl Love 

So, if you have examples where simplify is not idempotent, please post them. I am not saying there are none, but am saying that I am not aware of any in this moment (and I am in charge of simplify).

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Preben Alsholm 

There is no reason, it is just a historial fact. At the beginning, all dsolve(...) calls were requesting you to give the indeterminate function(s). Mathematica is still that way. I rewrote dsolve in 1997 and introduced the approach I used formerly when writing pdsolve, that is: get the indeterminate(s) from context. Then (only) dsolve/numeric also fell in my hands and so the same. I'll see if we can have the others also getting the indeterminates from context, it makes all the sense.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@SandorSzabo 

I didn't think about that when doing the previous change, but yes, it makes sense, and is possible to do it. I'll change the code a bit more.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Carl Love 

Taking advantage of your initiative of collecting things that still need some adjustment, there is also some extra parenthesis in the translation of worksheets ... see for instance the last answer (by myself) in http://www.mapleprimes.com/questions/200052-How-To-Apply-Dsolve-To-Set-Of-Diff, and in the right-hand side of (5) you see a matrix where each line is displayed enclosed between square brackets []. Those brackets are spurious - not there in the worksheet - download the worksheet and give a look at the same equation (5).

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Gaia 

It doesn't matter what a book or whoever says. These things are of the form 1 + 1 = 2. The equation 'result' you show, that is, "2*lambda1(t) - lambda2(t) + 2*lambda3(t) = 0", is not a consequence of the system [a, b, c] you showed in your first post in this thread. There is no doubt about that. Lift or OreModules, or for the case whatever else, cannot prove otherwise. It is not that we are guessing here. As said in the first reply, enter PDEtools:-casesplit([a, b, c]) and you see that the result involves a third order differential equation for one of the lambdas. This differential equation is not included in your equation 'result'. In the same way, as said in the first reply, enter PDEtools:-casesplit([a, b, c, result]), so now the four equations, and you see that the only solution is the three lambdas = 0. So the systems [a, b, c] and [a, b, c, result] _have not_ the same solution, your equation 'result' is not a consequence of [a, b, c] and, therefore, your question on "how to obtain the equation 'result' departing from [a, b, c]" has for answer that there is no way to do that.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Gaia 
You cannot get "2*lambda1(t) - lambda2(t) + 2*lambda3(t) = 0" from the system [a, b, c]. I tried to make that clear in the previous reply. Your system [a,b,c] is equivalent to a third order differential equation for one of the lambdas, plus two equations giving the other two lambdas in terms of the first lambda and its derivatives. On the other hand, your equation 'result' is linear in the three lambdas and involves no derivatives of any of them. If you add 'result' to the system, the only solution is all of them equal to zero. Therefore, result is not equivalent to [a, b, c].

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Hi
Thanks, Markiyan, for posting the info regarding the previous comparison 2 years ago, between Mathematica 8 and Maple 15. The way I see this comparison, two things step forward:

• Mathematica: has weaknesses with nonlinear equations and with linear equations that have nonrational coefficients. The slowness of their solver is prominent. They have known about all this for more than 10 years but the status of things doesn't seem to improve.
  
  
• Maple: is strong in solving linear and nonlinear ODEs for more than 10 years and is getting stronger at every release by developing original algorithms beyond Kamke's book. This is not a minor thing. Give a look at the pages ?updates,Maplexx,DE for xx from 8 to 16 and also to ?updates,Maple7,symbolic. 

One could argue that these observations are not really "news", that one could infer the same from the previous comparison two years ago. It is true. Still I think it is a relevant piece of information to confirm that this continues to be the case today (2013), that Maple is far ahead of Mathematica in solving differential equations also using the latest Maple and Mathematica releases.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

This tweak in the new (rewritten) simplify/conjugate resulted easier than expected. The change is in place and available for download in the usual  the "Maple Physics: Research & Development" webpage.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

This tweak in the new (rewritten) simplify/conjugate resulted easier than expected. The change is in place and available for download in the usual  the "Maple Physics: Research & Development" webpage.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

I'm glad to see that, both, you got this working the way you need and we got these commands enhanced in different ways. Looking at your coefficients.mw it also springs to my mind that some of your requirements could be options to Coefficients, as in Coefficients(expression, PhysicsType:-xxx) to select all the coefficients of objects of type PhysicsType:-xxx, further allowing to indicate the degree(s), as in Coefficients(expression, PhysicsType:-xxx, N), where N is explained in the Calling Sequence in ?Physics[Coefficients]. That would have saved the need for coding the coeffxxx functions you show in the mw. I will implement this as soon as I find some free time.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

I'm glad to see that, both, you got this working the way you need and we got these commands enhanced in different ways. Looking at your coefficients.mw it also springs to my mind that some of your requirements could be options to Coefficients, as in Coefficients(expression, PhysicsType:-xxx) to select all the coefficients of objects of type PhysicsType:-xxx, further allowing to indicate the degree(s), as in Coefficients(expression, PhysicsType:-xxx, N), where N is explained in the Calling Sequence in ?Physics[Coefficients]. That would have saved the need for coding the coeffxxx functions you show in the mw. I will implement this as soon as I find some free time.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Carl Love and Alejandro

Thanks for the info, so this macro suggested fixed the problem - I think I then know what is causing it. I'll fix it at its root in the first Physics update this week.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Hi

I use a macintosh, perhaps you do not and this is why I am unable to reproduce it. Could you please enter, at the maple prompt, the following: macro(``=``, ` ` = ` `) and let me know whether it fixes the problem. 

Edgardo S. Cheb-Terrab
Physics, Maplesoft