@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 Classic is obsolete, not maintained, and misses the extended typesetting (third paragraph, below) that exists in the Standard GUI, so I don't use Classic anymore, actually since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.

@Stev Eland 

The help pages were not revised, that is not what I said. What I said is that the problem - that generated the `*` display issues in the help pages - got resolved. That same problem would appear if you run a computation using DifferentialGeometry without updating your library (the one distributed in the Maplesoft R&D Physics webpage). It is fixed. If then you want to read a DifferentialGeomtry help page that you currently see with this display issue (unexpected `*` around), what you can do is to first install the update distributed, then open the page as a worksheet and execute the examples - that automatically reproduces the output with the new library and so without that display issue.

Next question: the instructions you read are about installing the mla file, that updates the library. So, no they do not help you in installing an update for help pages that is not distributed nor mentioned in the instructions. So according to the instructions the file you need to install is Physics2015.mla. 

The "PhysicsUpdate.mw" was so large at some point that got just discarded. Still, you can read about what is found in the update distributed by reading what is new in Physics in Maple 2016. All that is in the update of Physics for Maple 2015.

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

@sjaryal 

This time, I see the metric. Great. To conclude the computation you just posted in the file Weyl.mw, add, at the end of your worksheet, the following input lines:

Set the tetrad metric to null form

> Setup(tetrad = null);

Turn off automatic simplification to speed up matters (probably not necessary, but the result is large, so in this case it is faster)

> Setup(auto = false)

Compute now the Weyl and Ricci scalars

> Weyl[scalars]

> Ricci[scalars]

The last two input lines return the results you asked in your comments to this post (see worksheet linked at the end). Whether they match or not the paper is a different issue - I didn't check that - but attached is the continuation worksheet with the output of the lines described above, so that you could do that check yourself.

Now, note from the definition (Weyl[scalarsdefinition] and Ricci[scalarsdefinition]) that the result depends on the tetrad you are using, and that, as mentioned in my first reply, the tetrad is defined up to a transformation (i.e. there is freedom in the way you can choose it), so you may want to play around with that, or simply enter the tetrad you want to use - then compute the Weyl and Ricci scalars as indicated in this reply. To enter the tetrad or transform it, please proceed as shown in my first reply in the other thread (above).

Weyl_and_Ricci_scalars_(completing_your_computation).mw

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

@sjaryal 

You need to post a worksheet with the spacetime metric itself. In the worksheet "nulltetrad.mw" you posted above, you are not showing the metric, nor a computating with Physics, but a sequence of computations using GRTensor only (note that GRTensor is not an official Maple package, I don't have it installed for instance).

Also, you have been saying in at least 3 posts that you were unable to enter a metric using Physics, but you didn't show  the metric you are trying to enter nor your attempt to do so in a worksheet - as said you have shown only GRTensor computations instead, and without showing the metric.

Please after you post the metric itself, all of it visible, I can help you. Otherwise, I'm sorry but there is no way to help you beyond what is shown with worksheet in the reply above (how you manipulate tetrads) and what is shown with worksheet in a reply to you in the other post (how to enter any metric you want, that is not in the database) where you asked about this too.

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

@sjaryal 

Weyl scalars and tetrads (both null and orthonormal), are automatically computed on background, on the fly, when you set the metric. For the tetrad, that is shown in the previous reply above, and enter Setup(tetrad = null) and you automatically see a corresponding null tetrad. You can work symbolically with the tetrad e_[a,mu] or with its components as shown in the previous reply above. For the Weyl Scalars, an example is given in the other reply to your question.

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

@sjaryal 

Yes, besides the predefined metrics (Minkowski, Euclidean, or any of the 971 metrics in the database of solutions to Einstein’s equations) you can set the metric, manually, to whatever (symmetric) you want, you can also set the tetrad metric (eta_[a,b]) to be orthonormal or null, combining that choice with any of the four different standard signatures, —+, +—, +++-, -+++, and, you can use the default tetrad set on the fly by the package, or you can set the tetrad to whatever you want as well. 

The Physics:-Tetrads package has a number of useful commands as TransformTetrad to perform any of the standard transformations (nullrotation of two different kinds, spatial rotations on the m and m_bar plane, boosts, etc.) as well as user-defined general transformations. The IsTetrad command can check whether a 4x4 matrix is or not a tetrad for the spacetime you have set, OrthonormalTetrad and NullTetrad compute what their names indicate with some options, etc. You may want to give a look at Physics:-Tetrads and related help pages linked there to get the whole picture.

Below is a random example of the kinds of manipulations described above, running in Maple 2016 with the latest Physics library update, setting a metric of no particular interest, just for the purpose of showing what I mean in the 1st paragraph.

Download SettingMetricAndTetrads.mw

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

@Stev Eland 

Adjusments in all the packages mentioned in the title of this reply (so not just Physics) are included in the single mla Maple library distributed in the Maplesoft R&D Physics webpage. Just install it as per the instructions found in the zip file and you see the display of `*` within DifferentialGeometry corrected. Make sure you download the file for Maple 2015.

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

@Markiyan Hirnyk 

You need to realize that this thread, started by Samir impeccably, is about "What is new in Maple 2016" and impresses Samir the most, and not about "How does Maple and Mathematica compare with each other" in "this", then in that", which by the way was already discussed in Mapleprimes, beyond the answers given to you above, e.g. explaining that Physics in Maple 2016 is not at all just about General Relativity as you said, and that nothing like the Physics package exists in Mathematica. So I suggest please, Markiyan, let's keep the focus of the thread, and you are invited to continue comparing the systems in every aspect you find relevant, please, in the corresponding threads, or if you feel strong about just open another thread. Thanks.

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

PS: (back from vacations).

@Markiyan Hirnyk 

You answered vv  saying: “2. You wrote "Great Physics". The Physics package is targeted on general relativity which does not belong to the mainstream of modern physics.”

With due respect, I disagree with you regarding both statements, you seem to be uninformed. For what is going on in theoretical physics nowadays check for instance this map of the problems and their relationship from Aug/2015 (by the way a very nice summary for whoever is interested):

Consider how many of the titles above have to do with general relativity (almost all of them). You may want to read the article itself. In very short: the unification of gravity with the other forces (as well as what does that mean for our definition of space and time - brilliant and accessible presentation by Nima, from Princeton) is one of the main problems today. In the same line, consider for instance the recent detection of gravitational waves hailed as "breakthrough of the century" (for some people this is even bigger than the detection of the Higgs boson).

Regarding the “Physics” Maple package, it is not targeted to general relativity - it just includes it. Since this has also been asked in the past by Ogilvie, I repost here a reply given in October in Mapleprimes:

Please let’s not forget that general relativity (GR) is indeed part of physics, and this post just happened to be about that, which doesn’t mean that physics in Maple is only about GR.

As people using the package know, Physics has basic and advanced functionality for Quantum Mechanics since it entered the Maple library, including a full implementation of anticommutative and noncommutative operators and functions, related operations (including functional differentiation), Commutators, Anticommutators, Creation and Annihilation operator commands, pre-defined and customizable algebra rules, a whole implementation of Dirac notation for vector calculus on a space of quantum physical states, … to mention but a few; the list of functionality available is really large.

Perhaps it is useful to point to some application examples on Quantum Mechanics posted in this Mapleprimes forum in the past, developed using the same Physics package (that today implemented this most thorough digital database in existence for solutions to Einstein's equations):

• Quantum Mechanics using Computer Algebra 
• Quantum Mechanics (II)
• Superfluidity in Quantum Mechanics

The following link is also interesting because it shows a balanced set of applications in different physics areas, and the section on Quantum Mechanics also features a subsection on the use of the Physics package in developing proofs regarding properties of operations between quantum operators, something I don't recall having seen before in any computer algebra system, commercial or brewed at universities

• Computer Algebra for Theoretical Physics

For completeness, this other link to a mini-course on computer algebra for physicists is somehow ambitious, in that it shows an entry point to using such a wide-range-of-areas package as Physics is, while at the same time it is a compact tutorial for people who - simply put - never used computer algebra

• Mini-Course: Computer Algebra for Physicists 

Note as well that "what is new in Physics in Maple 2016" is not restricted to the database of solutions to Einstein's equations.

(Returning to my vacations)

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

Today we added 74 more solutions and derived information to the database, and with that we finished the book! It is a set of 989 spacetime metrics (solutions) , the largest databse of solutions to Einstein's equations in the world. The metrics added today are from Chapter 34, 35, 36, 37 and 38.

At this point, not only all these solutions are digitized. More important: they were digitized within a computer algebra sytem, where they become "computationally alive", it is possible to work with them algebraically, symbolically (tensor analysis), transforming them, analyzing their properties or those of the transformed metrics, classifying them, computing their invariants, working with them using the tetrads formalism, and a large etc. This is a historic result, that involved the efforts of many people, not to mention the authors of the more than 4,000 papers in the general relativity literature that in turn were condensed by the authors of the "Exact solutions to Einstein's equations" book. 

As usual, in order to have this new development installed in Maple 2015, you need to update your Physics library from the Maplesoft R&D Physics webpage.

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

@wgraf 
My understanding of this is that Physics actually handles different metrics in a much more compact way than GRTensor does, not the other way around (you may want to check for instance the online help page for ?Physics:-g_). Also, not only you can define your spacetime metric (tetrads included) in any desired manner but, also: regarding the coded metrics that come with GRTensor, Maple's Physics has really much more metrics coded, actually it has the largest database of metrics in the world - nothing less.

So, I cannot help you in the conversion activity you mention, but if I were you I would give a look at all this; chances are that facing the task of updating your work is less time-consuming or error-prone than staying stuck with an old package that in addition, apparently, from what you say, conflicts with Maple in basic ways (sqrt). Regarding the "error-prone": note that you can enter a metric in Physics in so many different ways, including by passing the corresponding line element or just a matrix, so maybe you do not need to retype anything at the time of updating your work.

Anyway, the best wishes for your project.

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