@otaviosama 

In that case (remember also please for other questions posted here), it is important for you to indicated what you expect as right value, especially if you say "[Maple] Physics doesn't return the right value". Also, in your post I read PauliSigmaRules - that can produce missunderstanding if you (e.g. now) say the J[n] do not obey the anticommutation rules of Pauli sigma Matrices - i.e. the rules you posted as PauliSigmaRules are not actually the Pauli sigma rules.

Please update your worksheet with whatever missing information and we (re)start from there - I'm sure we can help you. Best.

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

@Rouben Rostamian  

Thanks for the feedback; this is already adjusted in v.450.

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

@Fereydoon_Shekofte @Christopher2222

I perceive this the same way as Fereydoon_Shekofte, indeed. And those are, for me, the main reason for a Stack-Exchange Maple forum. There is a TON of mathematics capabilities in the Maple system. Many of them don't even exist in Mathematica, while they would be of use for many people working with mathematics. Yet nobody knows about that - we only advertise it in Mapleprimes where - mostly - only exists Maple users see it.

Regarding the (for me genuine) concern about duplication, I imagine that temporary solutions (e.g. 1 or 2 starting years) on the lines of what Daniel Skoog suggested, or even having every SE-Maple automatically reposted here in Mapleprimes for those who prefer to see it here, and even perhaps the other way around too with automatic reposts in the SE-Maple would suffice.

Regarding searching (another genuine concern) the search field of Mapleprimes could easily (optionally or not) also search in SE-Maple. Maybe it is even possible to have it the other way around too. That looks to me as a matter technically easy to solve.

Another issue that I would mention is the possibility of posting the contents of a Maple worksheet in SE-Maple. I don't know how that could be resolved, but I am sure there is a solution (maybe a tweaked pdf format ... something to think, not a serious obstacle I think).

@nm and  acer

Thanks. From what you posted, I can see we can try. I do not see the roadmap, though; the main questions that spring to my head: "what are they expecting?" Is it a number of questions per day? Per week? Is it a number of visitors per week? Is it a number of posts? And whatever the qualifier is, is it along one month? One semester? One year? And when do they give the membership status? In a month? Six months? A year? 

The point is that without such a roadmap - with explicit qualifiers known - it is not possible to estimate the chances of success (this resembles me giving a problem to a student and not providing him all the information to solve it. I heated that when I was a student, and not doing that was my main flag when giving courses at university.)

Without further information, just in this dark, I can tell you my estimation: many Maple users would be interested in a stack-exchange Maple forum. I foresee the volume of questions/answers and posts getting bigger rapidly if compared with what we see in this moment in Mapleprimes.

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

Adam Ledger's proposal is quite appropriate, I think; stack exchange seems to me the way to go nowadays, and am willing to put some weight/time on this. I am not familiar with the details, maybe you nm could summarize here, kinda brief/succint road-map, what would be necessary for success? Thanks.

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

@Area51 

Yes, you can define (add) tensors using tensorial expressions as definitions: the left-hand side (lhs) is the tensor being defined, the right-hand side (rhs) is the tensorial expression. And yes, the rhs can also have contracted indices - the only requirement is that the free indices of the lhs and rhs are the same, naturally. For all that, see the help page for ?Physics:-Define. I also see you used Box; there is Physics:-dAlembertian, the galilean one, but you can define one in curved spaces as explained in the previous sentence.

If you don't know how to formulate your problem on a Maple worksheet using Physics, try to approximate as much as possible the input lines representing your problem, and please post the resulting worksheet and questions here again.

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

You need to post the problem, explicitly.

@a_simsim 

Andras

I mentioned I was going to write again here regarding your suggestion concerning Den Iseger's algorithm. We gave a look at the paper, with Katherina, and the three algorithms implemented work pretty well with all the examples, Table 1: Analytical test functions, and Table 4: Continuous Nonanalytical test functions, in both cases getting better accuracy; but do not handle those of Table 2: Two Discontinuous test functions. In brief, for these two discontinuous examples it is not possible to determine whether the accuracy is or not increasing, and then the numerical evaluation routine gives up. We are short of time but will see if we can still give Iseger's algorithm a try. If so, I will post again here. Thanks again for the reference.

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

@Mariusz Iwaniuk 

Thanks for your feedback. I looked at your seven examples. Your example 5 is taken from Table 2 of the paper by Iseger mentioned by Andras, a discontinuous example. Then examples 1, 2, 4 and 7 (with regards to tackling them using the methods implemented) are basically of the same type as example 5. You see that by looking at the form of the Laplace transform being inverted, or at the exact form of the inverse Laplace transform. These examples - the one from Iseger's paper is the best representative, I think -  result uncomputable (using the implemented algorithms) because for discontinuous inverse Laplace transforms it is sometimes not possible to determine whether the accuracy is or not increasing. We were yesterday discussing with Katherina the possibility of implementing one more algorithm for this case (basically, what Andras suggested).

Then your example 6 is a piecewise branching at t < Pi, and you ask the numerical evaluation at t = Pi. Such a case is always difficult, for any numerical algorithm. Your example 3 is however, different: the expression being (Laplace) numerically inverted involves the Zeta function, whose numerical evaluation is itself a difficult problem, and the expected inverse Laplace transform is equal to harmonic(floor(exp(t)), 2). I am not a numerical analyst (more like a theoretical physicist), but I tend to think that numerical methods for problems like your 3 and 6, where you have discrete numerical functions, or where you ask for the numerical evaluation at where the discrete function branches, are not the standard problem, and in any case, not the problems I am targetting in a first implementation round.

Summarizing, if we have time, we will try to implement Iseger's algorithm as suggested by Andras and with that handle the two discontinuous examples of Table 2 of Iseger's paper (that would handle your examples 1, 2, 4, 5 and 7), Your examples 6 and 3 may or not be automatically solved at that point; otherwise they will require computing the exact transform first.

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

@a_simsim 

Hi Andras,
Thanks for the reference. Below is a worksheet with the testing example - comparing numerical inversion algorithms - of the paper you just mentioned, But the values of the numerical parameters they used are not shown. Do you have them?

Download Example_from_Laplace_transform_numerical_inversion.mw

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

@a_simsim 

At least for this release, I don't intend to work further in a numerical inversion of Laplace transforms. The three algorithms implemented are good enough. It is also unclear that Iseger's algorithm is better than the ones of section 2 of this post, and there is still work to do regarding inversion algorithms for other transforms.

That said, I looked now at the paper by Den Iseger you mentioned (it is from 2006, same year of the one we used in our implementation, see the post above) and noticed it contains a Table 1 with results for the mean absolute error for a set of 8 test functions. As soon as I find the time, we will run the same examples using the implementation we developed using Euler, Talbot and Gaver-Stehfest, then compare with the results shown in the paper and comment here again.

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

@Mariusz Iwaniuk 

That is not what the post says. You can use evalf to numerically evaluate %invlaplace (as well as any other inert mathematical function)- that is what the post says. You can use MathematicalFunctions:-Evalf to select one numerical method among several ones implemented, for the mathematical functions that have this feature implemented - certainly the case of %invlaplace as the post says. Giving a look at ?MathematicalFunctions:-Evalf you see it is also the case of the four AppellF functions and the ten Heun and HeunPrime functions.

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

@nm 

Inert stuff: everything preceded by % is an inert representation of the object not preceded by %, and can be executed using the value command. It is a fantastic Maple feature. The diff, series, evalf, simplify and several other commands understand inert representation and can compute with them taking into account the mathematical properties of these objects even when they are unevaluated (inert).

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

@nm 

Download more_general_solution_in_v.433_and_higher.mw

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

@J F Ogilvie 

As I already said, the Maple Heun functions include numerical evaluation routines for them, actually sophisticated ones. That these routines can be improved, as everything else, does not change that fact. I also know that you are well aware of the existence of those numerical evaluation routines - you actually reported a couple of problems with them. Writing here in "fake-news" style saying things you know that are not true does not help your point. Anyway I am out of this conversation.