@Bachatero 

The update for the Physics package is distributed in the  Maplesoft R&D Physics webpage. There, below the "Download the research version of Physics", you read a date; in this moment: "Files updated on July 28, 2016", and the first zip, Physics.zip is for Maple 2016. There you also have the latest update for Maple 2015 (that includes most of the Physics developments done for Maple 2016) and the latest update for Maple 18 (that includes most of the Physics developments for Maple 2015).

I heard of some people having trouble with this page in connection with caches in the browsers - maybe that is the problem you experienced? If so try flushing the cache, or with a different browser.

Best

Edgardo

@Bachatero 

Sorry that I can't help with that. Unfortunately, it is very difficult to fix things retroactively, ie to make a fix work also for previous releases. The issue is that every package - in this case Physics - changes in sync with (relying on) other changes that happen in the library. Making a fix work retroactively thus would require also change the old library in other parts, which in turn would require making more changes in more other parts, etc. It is almost impossible.

Having said that, you can install the Physics update for Maple 2016 in a Maple 2015 installation, and many things will work (all those not relying on other changes). So depending on the computation you want to do, you may want to try - just be aware that some things will behave unexpectedly strange or just won't work.

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

@Bachatero 

So, now d_[mu](Dagger(Phi(X)) returns in terms of diff whenever mu is a numerical index, covariant or contravariant, and regardless of whether the spacetime is flat or curved.

As usual, the adjusted Physics library is available for download to everybody at the Maplesoft R&D Physics webpage, and only works in Maple 2016.

In case you are curious, the underlying issue: although with paper and pencil Dagger(Phi) or conjugate(Phi) is not a composite function, the computer algebra representation is, and so the code needs to decide (conventionally) on a canonical form (say diff@Dagger or Dagger@diff), an issue that of course does not exist with paper and pencil. In connection with that convention, d_ was returning without proceeding further to avoid contradicting it. In the case of a numerical index, however, the computation can be performed to the end regardless of that convention so there is no point in holding the computation.

By the way: there are no "programmer boys" at Maplesoft. Unless you want to call me a boy :) :) :) If the Physics package were stuff that could be done by programmers without understanding of the mathematical methods used in physics, we would probably have had it in place and finished a long time ago, and also in the competition, where still today nothing even partially similar exists. Somehow the same is the story of the Maple differential equation programs, the FunctionAdvisor, and of some newer special functions, the conversion network for mathematical functions, the assuming command, etc. No programmer boys.

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

@Bachatero 

This is a different problem, not related to the display of Phi(X) instead of the expected Phi, but about the design: why d_[1](Phi(X)) is automatically converted to diff but not d_[1](Dagger(Phi(X))). I will revise this and write here again.

And thanks for pointing to these issues. One thing is to put code together, another entirely different is to have the feedback that permits polishing this code again and again, as much as necessary.

Best

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

@Bachatero 

You are correct - I will give a look at this and write again here soon.

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

@Kitonum 
Just to recall, because is good news, that a fix to this issue is being brewed. For instance, in the example of this post, what we are considering would result in: when willmoss entered D(x) (0), directly in the input he would see D(x)*(0), so the `*` becomes visible, automatically. From a design point of view that aims at using a blank space as `*`, to have it displayed when it would be ambiguous (generally speaking, when the blank is followed by an open parenthesis) seems to resolve the problem well.

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

@Mariusz Iwaniuk 

"Exact solutions for PDEs with Boundary Conditions", not etc., is the topic of this post. I think the developments mentioned are fantastic, also that this is another area where Maple's performance is indisputably better, and independent of your or my opinion about the relative strengths of Maple and Mathematica in general.

Perhaps this is philosophical but I think there are two ways of reading a post. A) Is there progress? Growth? Are the novelties useful? Is the material presented interesting? Instructive? Is this post about facts? Or statements, without supporting facts? Or, alternatively, B) Is there anything else not done yet? Are there others who have done more in perhaps other areas?

Please don't misunderstand me, but I personally feel reading using B) glasses doesn't take you far, doesn't help you achieving long-term success. Regarding A), I wrote the post so it reflects my opinion about how to read and write one.

Anyway, regardless of the above I forwarded your statements.

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

@vv 

I understand u(0,t) is a typo. Otherwise, u(0, t) would be a "boundary condition" but then, generally speaking, there would be no meaning for the question "how to determine the PDE symmetries".

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

@John Fredsted 

symgen is for ODEs only. For PDEs, use the symmetry commands of the PDEtools package (check ?PDEtools, the section on symmetries)

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

Hi Арина Козлова

I am curious about this material. Is there a version in English? Thanks

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

@Mac Dude 

I note that the 1D versus 2D considerations, above and in previous posts, always pivot on the implicit multiplication issue: f(x) is a function but f (x) is a product. Besides that issue, having a b representing their product looks fine and desired (to me and from what I read also to mostly everybody).

Looking closer, this implicit multiplication 'ambiguity' is mostly related to "something followed by a space followed by an open parenthesis". For the rest, 2D input is actually fine: you can even input everything in 1D but within a 2D input line, and it works perfectly, plus it has basic mathematical typesetting. That ambiguity is the problem. But that can be fixed: suppose for instance you type "f (", and you didn't mean multiplication, it was accidental, but then the interface automatically inserts a *, so that what you suddenly see is "f*(", so if you didn't mean multiplication you can just go back and make it be "f(". And of course, if you type "f(", no multiplication is inserted, neither when you type "a b". Wouldn't that resolve 99% of the issue? I think so.

We are considering this and some other alternative solutions. Just remove this ambiguity. And then, at least for me, there is no doubt that 2D input, with powers represented as superscripts, and a number of other mathematical display features, is, well, a lot more attractive than the raw 1D fortranish/brownish thing. In fact, I also noted that everybody talking about their students mentioned that some or many of them prefer 2D input. I don't think it is random. Mathematical display is more attractive in general, and definitely easier to parse with our brains. Removing this ambiguity mentioned in the previous paragraph is - to say it in few words - the whole thing, I think.

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

Hi Scot

There is the Standard and the Classic GUI (Graphical User Interface). The more modern is Standard, and there you have two modes: Document and Worksheet; both work, by default, with 2D input and, of course 2D output. Classic is obsolete, not maintained, and misses the extended typesetting (third paragraph, below) that exists in the Standard GUI, so I don't use Classic anymore, actually since 2008.

Now, regarding input in Standard: in Worksheet mode, you can set, in the preferences, whether you want to have the input regions as in 1D input (so the font used is courier, raw, with no format of any kind, as in old Maple releases) or 2D input (times new roman, italic, and with some extra formatting features). I see three advantages in using the 2D input mode. First, in 2D, you can also input everything using 1D syntax, directly, and without seeing everything in raw courier font. The second advantage of using 2D input: when you type x^2, in 1D it looks as you see in this text, but in 2D the cursor moves up, and the '2' appears as a superscript, excellent! You can also use a blank space for multiplication (I like it, some people prefer to place the * there). Ditto for x__1, it displays in the input line subscripted; and some others. These are some very convenient display advantages. The third advantage: place the cursor in an input line, right-click and chose 2D-math -> convert -> 2D-math input, and voila: the whole line is entirely converted to 2D math, which when combined with extended typesetting (next paragraph) gives your input a look similar to fantastic LaTeX typesetting. For me, this by itself justifies using 2D, it is just great.

Regarding the output, both for Worksheet and Document modes, and always talking within the Standard GUI, you still have two options: typesetting = standard or typesetting = extended. You can choose them from the preferences, or enter in an input line: interface(typesetting = extended). The default is 'standard'. The difference: with typesetting = extended you have full mathematical notation for everything, from the mathematical functions to their inert representations, to everything in the Physics package and its sub-packages (Vectors and Tetrads). The Maple experience is just another thing, beautiful, my brain parses the material on the screen at high speed and I can work with papers or textbooks to the side basically with just the same notation.

Finally regarding worksheet or Document. Frankly speaking, the differences are not big in that, for most purposes, both suffice for typing text with formulas within and performing computations (the difference is similar to those between a BMW and a Ferrari when you actually want to just go to the supermarket). The Worksheet mode has some visual formatting clues, as the prompt where you enter a computation to be performed, and vertical lines to your left that identify input/output blocks and also sections, but you can hide these vertical lines too (in the menus there are options for that.) True: the Document mode (default) has additional features, but as said for most purposes both suffice.

My particular choice: I work with Worksheets because I prefer the "input/output" regions separated from the "text + math formulas" regions, I hide the vertical lines that are normally displayed to the left (View -> Show/Hide -> uncheck Section Boundaries and Execution Group Boundaries), they look like noise to me, then I use 2D input mode, but type everything using 1D syntax (it is easier to type and to spot mistakes), only omitting the * multiplication, and convert to 2D input when I like the input line with full mathematical display. And I use typesetting = extended always ON so that in the output I see EVERYTHING with mathematical textbook notation. It is a great experience.

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

@vv 

Due to developments in Maple's kernel for "Maple 2016", the impact is really none, In Maple 2015, however, Physics:-Assume does use more memory space to perform remember-tables cleanup operations, but the memory is returned to the system as soon as the cleanup is finished. The main difference is that in Maple 2015 the process is visibly slower. 

The operating mode of Physics:-Assume, that is: to place assumptions without redefining the variables, is to be an option in the old assume command. I think I mentioned that here in Mapleprimes time ago ...  can't remember the post now. The only reason for this option not being in place in assume is the myriad of other things that took my attention and time the previous year.

We have a similar situation with the new operation mode Physics:-Setup(assumingusesAssume = true) introduced in Maple 2016. After you input that, the assuming command automatically uses Physics:-Assume instead of assume, and that makes assuming fully compatible with Physics, DifferentialGeometry, VectorCalculus, etc. This too should be an option, in assuming.

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

@zhuxian 

After

> coeffs(expand(pd2[1]), du);

Enter

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

@John Fredsted 

" ... I still (having said it before) miss some form of text book material on the Physics package"

Yes, I remember you asking about this. I need to give higher priority to producing a kind of e-textbook for Physics that would cover what you are asking. Meantime, note that there are mainly four different entry points.

One of them is, of course, the whole set of help pages. But then, there are 63 commands within Physics, 14 within its Tetrads subpackage, 145 within its Library subpackage and other 78 within the Library:-PhysicsType subpackage; in a situation like this, just the amount of help pages is discouraging ... Still, the pages (but for some very new commands and the PhysicsType subpackage) are thorough and contain many examples.

Anyway, the functionality in "Physics" covers "physics areas" and there is another entry point: the Physics, Examples help page, organized by areas, with separate sections for Vectors and Analytical Geometry, Mechanics, Electrodynamics, Tensors in Special and General Relativity, Classical field theory, Quantum Mechanics. Each of these sections contains solved problems, none of them trivial, illustrating the package in action. But then each of these areas is by itself large in scope (e.g. the reference for Quantum Mechanics itself is a two big textbooks discussing many different kinds of problems). It is difficult to cover well so many different areas.

A third entry point is the help page for Physics,Conventions, that presents the package from an entirely different angle, closer to 'the design point of view', and for many people, this is the most clarifying help page. This page, together with the Overview page for the Physics package, (with a summaryzed one line description for each command), the one for Physics:-Setup (this one is really key), and the applet that launches when you input 'Physics:-Setup()' give you pretty much details / control over everything.

A fourth entry point is the "Mini-Course: Computer Algebra for Physicists" , a mini-course I give from times to times, with 10 sections, the first five as in "Maple 101" and then from sections 6 to 10 all about Physics, with presentation and solved examples.

I think all this is really good documentation, and where it is incomplete it is because the package is developed at a speed that makes difficult to keep the documentation always "up-to-date". But on the other hand I agree entirely with you that at this point a compact e-book, getting the best of all the above and complementing where necessaary, may be more useful and the way to go. I'll do my best to separate the necessary time for this. By the way a similar situation happens with PDEtools.

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