@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

Hi

Maple 17.02 is available for download.  Just to note that 17.02 includes various improvements in 'Physics', basically all the work done in the package till August 20, though none of the posterior improvements mentioned here in Mapleprimes, available for download at the Maple Physics: Research & Development updates page (latest update: today). These posterior improvements are described in the PhysicsUpdates.mw distributed within the zip file together with the update.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

In the help page you read "The select(e, f) selects the operands of the expression e which satisfy the Boolean-valued procedure f". The key observations are that you select "the operands" and you do not change the container - ie the type of the e containing the operands (but for some special cases of automatic simplification: e.g. the product of a single operand `*`(a)  becomes the operand itself and so it is not a product anymore).

Now in your last reply, phi = Ket(psi, 1, 1, 0). So select(phi, commutative) will return Ket(1, 1, 0) (because only psi is not commutative), then select(type, phi, PhysicsType:-Ket) will return Ket() because none of psi, 1, or 0 are of type PhysicsType:-Ket. Understanding those you also understand how the other results you show are formed.

In brief, that is how select works, give a look please at the help page ?select and its examples.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

In the help page you read "The select(e, f) selects the operands of the expression e which satisfy the Boolean-valued procedure f". The key observations are that you select "the operands" and you do not change the container - ie the type of the e containing the operands (but for some special cases of automatic simplification: e.g. the product of a single operand `*`(a)  becomes the operand itself and so it is not a product anymore).

Now in your last reply, phi = Ket(psi, 1, 1, 0). So select(phi, commutative) will return Ket(1, 1, 0) (because only psi is not commutative), then select(type, phi, PhysicsType:-Ket) will return Ket() because none of psi, 1, or 0 are of type PhysicsType:-Ket. Understanding those you also understand how the other results you show are formed.

In brief, that is how select works, give a look please at the help page ?select and its examples.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

Just to point out that a new Physics:-Library:-Add command, free of these subtleties regarding the evaluation of arguments of sum or the use of local variables inside procedures related to add, is ready and included in today's Physics update.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

Just to point out that a new Physics:-Library:-Add command, free of these subtleties regarding the evaluation of arguments of sum or the use of local variables inside procedures related to add, is ready and included in today's Physics update.

Edgardo S. Cheb-Terrab
Physics, Maplesoft