Hi, could you please upload a worksheet with the metric? You can use the green arrow for that.

Hi
Wikipedia mentions the DiracComb function. Anyone has an idea of how frequently used is this function? Maybe it is worth implementing it in Maple. Opinions?

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

May 27: Answer and add a worksheet showing how to do this with Physics

First the answer to your question: change you input 

Oneform := RaiseLowerIndices(g, ON[1], [1])

by

Oneform := convert(RaiseLowerIndices(g, ON[1], [1]), DGform)

And that resolves the problem you encountered. Next is how you do the same computation using Physics

Download WithPhysicsTetrads.mw

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

In the latest Maplesoft Physics Updates (v.1235) there is a fix to "not placing the default nonnegint assumption" I mentioned a couple of replies above. So with the latest Physics Updates for Maple 2022, we now get

PS: @Carl Love, although I see the motivation for your comment, I don't foresee adding to the diff command an option like "return a piecewise with all the cases".  The design of diff is to return a default value, and handle assumptions when possible - only that. It is similar to how the conversion network for mathematical functions works (see ?convert, to_special_function).

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

@vv 
I pointed out that the symbolic differentiation result, for symbols j and k, is correct. You objected to that. I only replied showing that, indeed, the result is correct. That closes the question.

Next you pointed out that the symbolic differentiation result is fragile. That concept is debatable. I do agree though, with a previous comment by you, that the most common situation is j, k nonnegint; so if choosing a way to express the result using GAMMA functions, do that for the most common case. The symbolic differentiation code is already doing that. But not in one branch of a subroutine, and the problem posted hits that branch. Although the result is correct, it can be better. It is something to adjust.

But then you come up with applying blindly the manipulation I used for the default output, after (you) using the opposite assumptions. With due respect, @vv, I don't see your point. You realize that if the result contains GAMMA as in this example, under direct evaluation it will either work with j negint, or for j posint, and not with both at the same time.

Add to that my opinion, that returning piecewise functions all around is not a convenient idea. Instead, I prefer presenting results with a convenient default and leave to the user to use assumptions for the other cases. Also relevant: understand that having Sums, and especially in the higher-order symbolic differentiation case, the results may require additional algebraic manipulations when evaluating the symbols involved at some values; typically, cases where correctness would require using limits or removing apparent singularities.

Returning to your example assuming j::nonegint, k::nonegint (above this reply), the manipulation after ex1 is as follows:

So, the result by the symbolic differentiation code is also correct when assuming j::nonegint, k::nonegint.

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

@vv 

Download Symbolic_differentation_is_correct.mw

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

Hi @vv 

The problem you point at is in `eval/Sum`. Not in sum and not in D, both work correctly, that is why D[1$2,2$4](f)(0,0) returns 6, correct. To see the problem in `eval/Sum` try

f := (x, y) -> 1/(2 + x*y^2):
D[1 $ j, 2 $ k](f)(x, y);  # correct result for the jth and kth symbolic derivative

                                ...

eval(%, [x = 0, y = 0]);  # problem in `eval/Sum`
                                   /   k     \
                                   | -----   |
                                   |  \      |
                 pochhammer(-j, j) |   )    0|
                                   |  /      |
                                   | -----   |
                                   \_k1 = 0  /

PS: when using the Green Arrow to insert a worksheet, you can also ask for the contents to be shown, and filename.maple are not recommended for upload; use filename.mw instead.

Download SubstituteOperator_(II).mw

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

@etian2 

But then you need to write the preamble properly - and that is not what you are doing. One workaround is for you to convert any worksheet, get the right preamble, then use it as a template. If that doesn't work AND you keep not posting a worksheet (do you expect people to start reading your image and trying to reproduce by typing etc.?), there is no chance.

Anyway, this is my last reply to this thread.

@etian2  I don"t see your worksheet. Also, the heading of the file you show is not the one you get ia File >Export> Latex. 

@etian2 

From your answers, guesswork is not helping. Let's move away from guessing. Could you please post the worksheet you are translating to LaTeX? I will give it a look.

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

@etian2 

In usepackage, it is maple(.sty). Not maple2e(.sty). Yes you need to copy the sty files to the directory where you put the tex file, that is the standard LaTeX procedure for sty files.

@etian2 

type a_ + b_ anywhere, say within the text. Then mark the equation with the mouse, right-click, convert to > 2D-math non-executable, and you will see it with the arrow on top, as you say, symbols in nonexecutable math.

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

@etian2 

I imagine you did not input kernelopts(mapledir) to see what directory the help page is indicating - Is it that? So, enter kernelopts(mapledir) at the Maple prompt, see what directory it indicates, open the file manager there and you will see a subdirectory called "etc", within which there is maple.sty. All Maple installations are the same.

@greatpet 

I'm glad to hear that more people are excited about Maple's developments in theoretical physics. Your comment is an opportunity to shed some light on what this is about - why the words I used in this post.

Note first that four different packages converge in this development: FeynmanDiagrams, FeynmanIntegral, Physics, and new in Maple 2022: StandardModel. These packages were all developed in consultation with actual practising theoretical physicists; see the Maple Physics: Research & Development.

The FeynmanDiagrams and FeynmanIntegral packages both involve several commands for performing all or each of the steps of the computations of scattering amplitudes and Feynman integrals. We do that in both coordinates and momentum representation - feynarts cannot do that. Then FeynmanIntegral performs (with restrictions, however) the symbolic computation of these integrals, which is also not possible with the packages you mention. FeynmanDiagrams and FeynmanIntegral implement relevant functionality available in computer algebra for the first time, presented in Computer Algebra and Particle Physics - CAPP 2021.

Now, it is true that we didn't contact the authors of the packages you mentioned. But there is a reason. All but one are implementations in Mathematica. Still, two papers are being finished about FeynmanDiagrams and FeynmanIntegral, and as is standard in these cases, both papers include tables comparing functionality - and yes: there we talk about the packages you mention. By the way, about FeynRules (feynrules.irmp.ucl), note that in the Maple implementation, due to having functional differentiation available as a command, the Feynman rules are computed automatically, on the flight, for any possible QFT model, turning unnecessary a package for just that.

The fourth package you mention is implemented in FORM, not a general-purpose computer algebra system. It is not possible to implement in FORM something like what you see in Maple Physics even if you restrict the goal to what is shown above for this new StandardModel package.

Perhaps more important, each of FeynmanDiagrams, FeynmanIntegral, Physics and StandardModel has several commands that can work in black box or all the steps approach. When compared with previously existing software in other platforms, four things in this Maple Physics environment appear to be unique:

• The implementation has an emphasis not just on research but also on education. That is what I meant with all the steps approach.
• The notation, both for input and output, is basically as in textbooks to the point that during presentations, sometimes people ask whether I am showing LaTeX or Maple. That this notation includes functional copy (from output) & paste (on input) increases the usability significantly.
• Things can be set and changed effortlessly. For example, you can set the interaction Lagrangian for a model in 1/2 line (no need to write a text file as with feynarts) and compute scattering amplitudes in coordinates or momentum representation right away. For the StandardModel, we added a command, Lagrangian, to retrieve its different sectors or all of them. This command is relevant due to the large number of terms of the model, and because of the several different kinds of tensor indices necessary to algebraically represent it.
• The implementation of mathematical objects and related operations starts at a very deep level. Both the differentiation and product operators are redefined entirely. They handle noncommutative, anticommutative and commutative objects as we do with paper and pencil, including in that user-defined: tensors of different kinds, differential, Hermitian, Unitary, etc. quantum operators with their properties, commutator algebra rules, disjointed Hilbert spaces, etc. No wonder why for Maple 2022 we were able to implement the new StandardModel package; it is built on top of all that.

This is the help page of StandardModel-Lagrangian.mw; it illustrates the itemization above.

While, in general, I'd agree with you on the meaning of "a remarkable achievement in computational physics", the capability to represent such different mathematical objects with their properties set, as well as to perform such different operations with them in so a versatile way and so similar to what we do with paper and pencil, all that I think is indeed a remarkable achievement in computational physics. 

Finally, regarding performing previously impossible novel calculations published in peer-reviewed journals, while that is possible, our approach is, as said, to implement both education and research-level capabilities with the bar as high as we can see (and for that, yes we take a peek at the existing software). In this way, it is possible to achieve a remarkable computational implementation independent of having already a previously impossible result at hand.

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