@John Fredsted 

There seems to be a bug in assume: after you assume(theta1(t,x,y,z),scalar): and assume(theta2(t,x,y,z),scalar): I would expect getassumptions(theta1(t,x,y,z)) to return {(theta1(t, x, y, z))::scalar} but instead it returns {(theta2(t, x, y, z))::scalar}. From that output, Dagger cannot conclude about theta1(t,x,y,z) and so it returns with dagger instead of conjugate.

The solution to all this is to have one more option in Setup, as said, to indicate that something is scalar, even an algebraic expression perhaps more general than a function. One of the advantages of this approach, as the one already in place to indicate that something is real, is that it does not change the object into something else and therefore you can reuse expressions involving the assumed objects that were entered before the assumption got placed. Likely, you can remove the assumption at any point and reuse expressions entered while the assumptions were holding. All this because when you Setup(real = {a,b,c}) there is no change to a, b or c. 

Have in mind however that I'm somewhat overloaded with activity related to the upcomming Maple release - will probably only be able to implement this new setting in February ...

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

@Carl Love 

In the previous reply I meant this could be done taking the standard `print/diff` (the one there when you restart) as template, but you can also change the one installed by `PDEtools/declare` instead - in fact it is probably easier, despite that the routine is much bigger. So in that case look right after line 92 as shown by showstat: the local variable called tty_ans is the f[x,x,x,y,y] object; insert a couple of lines there to convert to tty_ans := f[3x, 2y]. Note however that if it is a function of only one variable and that variable happens to be the prime variable tty_ans is not an indexed object. To workaround that situation, search for things like ... if dx = prime_variable ... and replace that equation that involves 'prime_variable' by the word false.

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

@Carl Love 

Take as template the `print/diff` of Maple 17: right after line 20 as shown by showstat(`print/diff`) starts a loop that does most of what you need - a small alteration in the conditional that starts at line 24 would suffice.

Having said that, note that `print/diff` is changed on background by a number of packages in order to display things according to the increased functionality they provide; this is the case when you use PDEtools:-declare and also Physics.  Next, have in mind that the display is one thing, the copy & paste is another one, and if you want the latter to work you need to use something else, e.g. Typesetting:-mcomplete. Finally, print/diff is an internal routine, it changes frequently (e.g. its size for Maple 18 multiplied by two) in order to accomodate new functionality, so just be aware that what you write and works in one release may be conflictive with the print/diff of the next release ... as said these are internal routines, that is the way it is for them.

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

@peter137

Thank you for your comments. There is a vision behind this project and it's coming along nicely. And yes, updates for the Physics package are being posted around the clock, serveral times a week. Our goal is to accelerate the development with rapid ping-pong-like feedback - with the results available for download right away, and mainly to move the focus into what people are actually doing with the package today. Things like what you see in the two previous posts on Quantum Mechanics (here and here, the third one comes next week) illustrate not only what we can do today with this package but also how constructive this new developmental approach of presenting updates around the clock is.

I wrote a first draft of a book on the use of Physics a long time ago, when this was a University project. It was rather popular among students. I considered updating and completing it many times, but have not had the time. Hopefully, I'll be able to complete it during 2014.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Sergio Parreiras 

Hola, :) I'd need the actual Maple input for dsys; you could either paste it in 1D or attach a mw with the 2D input. Advancing: it is not possible to set an independent variable as arbitrary, but there may be ways to achieve the same thing -I need to give a look and with a concrete example to think about is simpler. Also the error interruption is not appropriate, that requires a fix. Y gracias por el feedback Sergio! :)

Best

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

@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