@Michael_Watson 

Maple_Question_7.8.14_(reviewed).mw

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

@Alejandro Jakubi 

Just to clarify: the R&D udpates for Physics, Differential equations and Mathematical functions, are official Maplesoft updates. These  R&D updates pass through all the related Maplesoft internal test suites before being posted in the R&D pages for download. These R&D updates are however different from the more general dot updates in that R&D ones have not passed through beta testing as the dot updates do, and for that reason the R&D updates mechanism is so much more agile. In Physics, for instance, we frequently have one or more updates per day.

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

@oldstudent 

I am not sure about your question: if you refer to the "DEs and Mathematical Functions Updates" mentioned in the title of this post, this update is already available for download for everybody in the Maplesoft R&D Differential Equations and Mathematical Functions webpage. This update, together with the update of the Maple Physics package are currently distributed only as a download from these two webpages, so you do not get them via tools -> check for updates.

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

@Alejandro Jakubi 

The status is: work in progress. I preferred to start where the gaps were bigger, clearly the 42 elliptic functions. Not what you asked but anyway some details: these "elliptic functions" include the 13 JacobiPQ, 13 InverseJacobiPQ, JacobiZeta, the 4 JacobiTheta, the 4 Weierstrass, and then the more familiar F, E, E', K, K', Pi and Pi' - 7 functions for which, in addition, we have an issue with their definition implemented in Maple in the 90's: it is non-standard, making things more difficult, because there is basically no literature to consult that uses these definitions.

There is always the issue of 'backwards compatibility" to consider but, generally speaking, the natural thing would be to go ahead redefining these F, E, E', K, K', Pi and Pi' elliptic functions according to the literature, resolve any differences by always following the modern and thorough NIST Digital Library of Mathematical Functions project, and finish with this historical issue in one go. The NIST project is the XXI century continuation of the work by Abramowitz & Stegun, Gradshteyn & Ryzhik, Bateman, Byrd & Friedman, P.B.M, etc..

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

@Alejandro Jakubi 

Thanks; it's fixed now. Regards.

Edgardo

@oldstudent 
I added below an incomplete list of Maple strengths that in my opinion disproves your conclusion.

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

@USPAS2014 
Just about your comment on availability: the mini-course is linked in the Maplesoft R&D Physics webpage. - last link in the column on the right.

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

@Alejandro Jakubi 

Indeed I do have it my .mapleinit. About having this as a new command: generally speaking, when certain functionality can be used through options we will not add it as a new command. This case however is one where the combination of arguments is cumbersome enough and the functionality is used frequently, kinda justifying an exception. I forwarded now your suggestion to the people who take care of plots.

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

@rashmi 

I understand you can perform this computation in current Maple 18, but am not sure if the DifferentialGeometry package in Maple 12 could help you for that purpose, probably yes, give it a try. The starting point would be the help page ?DifferentialGeometry,OverviewOfGeneralRelativity.

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

@trace 

I will have time to give a look at your paper by Friday, hopefully before that. By the way nice worksheet the one posted by Torre using the DifferentialGeometry package for this problem.

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

@trace 

I am not sure I understood your worksheet as you intended, here are two possible interpretations. In the first one you seem to want to set the metric as your expression (2)

> (dt+4*w*(1/m^2)*(sinh((1/2)*(m*r))^2)*dphi)^2-sinh(m*r)^2*(1/m^2)*(dphi^2)-dr^2-dz^2

and then compute the value of Ricci[2,2]. If this is all what you want, and assuming that the coordinates are already set, just enter

> Setup(metric = %)

And the value of Ricci[2,2] is then given by

> Ricci[2,2]

And that is all. 

If however your question is about how to perform a transformation to then compute Ricci[2,2], suppose then you want to perform a transformation on a tensorial expression, and by that I mean you have the set of transforming equations, say tr, with the old variables on the left-hand sides and the new variables on the right-hand sides, or the other way around (new = old instead of old = new). Suppose now that you want to compute the components of a tensorial expression in the new coordinates, for example: the component [2,2] of the Ricci tensor. This is the sequence of steps:

1) transform coordinates on the spacetime metric

> TransformCoordinates(tr, g_[mu,nu]);

The output will show up in matricial form. If you prefer to see it as the square of the line element, then pass also the optional argument 'output = line_element'. Either way, if the output is according to what you expect, then:

2) set this result as the new value of the metric

> Setup(metric = %);

And that is all. You can now compute the value of any tensor directly, for example, as in

> Ricci[2,2]

The relevant thing then is the transformation tr. Reading your worksheet I have the impression you meant to use a transformation that can be represented in matricial form by

> M := Matrix([[1, 0, 0, 0], [0, sin(m*r)*(1/m), 0, 0], [0, 0, 1, 0], [0, 4*w*(sinh((1/2)*(m*r))^2)*(1/m^2), 0, 1]])

Am I understanding your worksheet correctly? Note also that the ordering of coordinates I am using is [r, phi, z, t], so t is the 4th, and hence also the 0th coordinate - this is the convention in the Physics package: all 0th components are entered as 4th components and you can refer to them using 0 or 4, as you prefer.

I noticed also that the first two lines are not actually equal: simplify((1)-(2)) does not give 0 - I am not sure whether that is consistent with what you present).

In summary: I suggest you to write the transformation explicitly and then use TransformCoordinates. Please feel free to ask again if you cross with obstacles; I'd be interested in seeing your development.

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

@trace 

Thanks for posting your worksheet mm.mw; the answer appears further below

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

@trace @escorpsy

Download mmm_(reviewed).mw

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

@Alejandro Jakubi 

Generally speaking I agree with what you say about Solve and solve, and in fact that was the original idea, many years ago, when I mentioned this project of a "unified solver" to Keith Geddes. I also agree in that the so-powerful differential elimination packages in Maple are almost invisible to the average user. About an interface for them, however, I think PDEtools;-casesplit is just great, easy and as intuitive/friendly as it could get. It would be more used if it were top-level though, the same as PDEtools:-Solve.

But that picture is incomplete: Both dsolve and pdsolve make extensive use of these two 'invisible' differential/algebraic elimination packages, and also of the differential-polynomial-forms introduced with PDEtools:-dpolyform and PDEtools:-casesplit. So, through dsolve and pdsolve everybody end using these fantastic packages and the extra functionality provided while interfaceing them, even if the packages are somehow invisible to the average user. And the differences between the solving power of dsolve & pdsolve in Maple versus DSolve in Mathematica are rather well noticed by mostly everybody.

Likewise, the solve command has incorporated a few years ago a lot of elimination functionality from the RegularChains package, to some point a sort of algebraic equivalent of the DifferentialAlgebra package that also handles inequalities. And so through solve mostly everybody now take advantage of RegularChains, also an almost invisible package. By the way there is no facilitating interface for RegularChains. For some time I've been thinking of extending PDEtools:-casesplit to also (optionally) interface RegularChains for handling non-differential systems.

Taking all into account, I don't see the picture as grim as you seem to present it. I do believe mainly that a step forward would be to make top level both the the concept of a unified solver (PDEtools:-Solve) and this general 'split into cases' command (PDEtools:-casesplit). Beyond what they unify or interface, both commands also bring new functionality that is highly regarded and just not available elsewhere in Maple or other computer algebra systems.

By the way I don't see how could I help you but it is unfortunate that you stopped posting.

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

@trace 

Look, you need to show what you wrote so that one could give an opinion, for instance whether "R_0,rho,alpha,beta R_0^rho,alhpa,beta" or "R_1,rho,alpha,1 R^rho,alpha , Riemann[1,rho,alpha,1].Ricci[rho,alpha]" are correct. Also, correct with regard to what?

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