ecterrab

J F Ogilvie You have a very p...

Answered: ecterrab 14702

December 07 2018

2 0

You have a very peculiar way of expressing your points of view ... I will disregard that for this one time and try to help you with the contents.

The Maplesoft Physics Updates work fine with TTY cmaple, and also with the Standard Interface distributed with Maple, maintained by Maplesoft, and also with the not-maintained-anymore-since-years, so-called "Classic," ancient interface, the one you say you want to use, that was developed in the 1990s, provided that Maple itself runs properly in that interface.

IMPORTANT: the Maplesoft Physics Updates require you to have installed the latest Maple version (2018.2.1). If that is not the case Maple will warn you and point to the webpage from where you can download a version of the Updates for your version of Maple.

Now, that there are other things in that ancient "Classic" interface not working the way you expect, as you are saying, would seem expected for me, for the reasons mentioned in the previous paragraph. That is also not related to physics or my person: as you pointed out in your post, Maple 2018.2 is already having trouble to run in that not-maintained ancient interface. Interfaces developed more than 20 years ago typically don't work 100% or at all in nowadays operative systems, a situation standard in software. You could still argue that "Classic" is included in the distribution of Maple (not for Macintosh since many years). Yes, but you know it is not maintained anymore and that is not the interface Maplesoft indicates to use with the Maple system, since years.

Then if for you, using the ancient "Classic" interface, is relevant for any reason, working with the last Maple that runs fine for your purposes in that interface would be the way to go, I suppose. Otherwise, I suggest you to start using the Standard interface, distributed with the Maple system, intended for its use, and well maintained by Maplesoft.

Maybe of help for you in that transition: open the preferences of the Standard interface, the one distributed with Maple and maintained by the company, and choose to use worksheet instead of document mode. If you prefer, also choose to use 1D math input (so-called Maple Notation). These two things already make the Standard interface distributed with Maple nowadays work primarily as that ancient "Classic" one, as said not recommended and not maintained anymore for many years. If the remaining differences are still important for you then, unfortunately, I have nothing else to suggest you.

Physics Updates version 240....

Answered: ecterrab 14702

December 06 2018

3 4

Hi John

This difference in behaviour between `.` and Physics:-`.`, for A^n (n an integer) when A is the computational object Array of dimension 1 or 2 is not present anymore after installing the Maplesoft Physics Updates version 240 or higher. Arrays (for which type(A, Array) returns true) are now kept unchanged, not rewritten as the object Matrix.

In that sense, this is now adjusted for good, or fixed, depending on whether you see this as an undesired incompatibility (my take on this nowadays) or a bug.

As for the origin of this problem: the same way you - somehow - found "natural" (say?) that for a 2x2 table of numbers the object A^(-1) would satisfy A . A^(-1) = Identity (number 1 in the diagonal, the rest equal to 0), I also found that natural 15+ years ago when coding this.

But if A is represented using the computational object called Array, then A . A^(-1) is not equal to the Identity but to a square table of numbers all of them equal to 1. The first time I saw this I thought it was a bug. As Pascal4QM says, for the computational object Array, `.` is performing elementwise multiplication. As a physicist, I thought this behaviour was undesired, prone to mistakes. Whether you represent the square table of numbers using the computational object called Array or the one called Matrix (and both are displayed the same way on the screen - as a square table of numbers), in mathematics, the dot product of square tables of objects is called matrix multiplication, not elementwise multiplication. So, in Physics:-`.` day one I also coded a convert(A, Matrix) when A was the object called Array before proceeding with the "multiplication" of square tables of numbers.

And nobody ever complained about this or found it unnatural for 15+ years, but today (this post by you).

Looking at this design issue today, it also seems to me relevant to keep the differences in behaviour - sometimes unavoidable - to a very^2 strict minimum. So the adjustment mentioned at the beginning.

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

Solution - not hanging....

Answered: ecterrab 14702

November 26 2018

6 0

Hi nm,

The problem Maple had with this example was not in whether the boundary conditions are of Neumann or Dirichlet kind nor in whether they are nonhomogeneous.

The problem was in the presence, in the PDE, of an unknown function as , depending on both x and t. You realize that can make computing the solution particularly difficult, specially if you have to match that solution to boundary conditions also of the most general form, depending on arbitrary functions, here and .

On the other hand, I agree with you, the code should not try to do impossible things, e.g.: separation of variables in the presence of an unknown function of both variables like. Having adjusted the code now (this adjustment is already within the distributed Maplesoft Physics updates version 223 or higher), the computational flow moves forward, the problem is within the scope of the methods implemented.

So this is the problem you posted:

>

ic := u(x, 0) = f(x)
bc := eval(diff(u(x, t), x), {x = 0}) = A(t), eval(diff(u(x, t), x), {x = 1}) = B(t)

And this is its solution:

>

(1)

To follow the computational flow, enter before the call to pdsolve above.

Download solution_-_not_hanging.mw

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

Fixed in version 201 of the Maplesoft Ph...

Answered: ecterrab 14702

November 26 2018

6 0

Hi nm,

Good catch. This problem is present in 2018.2 without the Physics Updates. A fix is already uploaded for everybody within the Maplesoft Physics Updates version 201 (or higher).

>

(1)

>

pde := diff(w(x, t), t)+3*t*(diff(w(x, t), x)) = w(x, t)

>

(2)

>

(3)

Note by the way this problem can also be solved using Fourier transforms

>

(4)

>

w(x, t) = (1/2)*exp(t)*(Int((Int(f(x)*exp(-I*x*s), x = -infinity .. infinity))*exp(-((3/2)*I)*t^2*s+I*s*x), s = -infinity .. infinity))/Pi

(5)

Download Fixed_in_Physics_Updates_version_201.mw

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

PDEtools:-DeterminingPDE and DEtools[ini...

Answered: ecterrab 14702

November 26 2018

3 0

Not necessary, but useful to avoid typos and better readability, enter your PDE using PDEtools:-declare and PDEtools:-diff_table ,

>

(1)

>

Input now the ODE directly using jet notation

>

(2)

Now on your question: How do you check the dimension of the underlying symmetry group, or whether it is finite or infinite? You do that by:

1.	compute the determining system for the Lie symmetries of the problem;

2.	check the dimension of the solution of that determining system.

For the first step, you can use DEtools[gensys] or PDEtools:-DeterminingPDE

>

${diff(diff(diff(_eta[v](u, v), u), v), v) = (-(diff(diff(_eta[v](u, v), u), v))*v+diff(_eta[v](u, v), u))/v^2, diff(diff(diff(_eta[v](u, v), v), v), v) = (3*(diff(_eta[v](u, v), v))*v-3*_eta[v](u, v))/v^3, diff(diff(_eta[v](u, v), u), u) = 2*(diff(_eta[v](u, v), u))/u, diff(diff(_xi[u](u, v), u), u) = (2*(diff(diff(_eta[v](u, v), u), v))*u^2*v+2*u^2*(diff(_eta[v](u, v), u))-2*v*(u*(diff(_xi[u](u, v), u))-_xi[u](u, v)))/(u^2*v), diff(diff(_xi[u](u, v), u), v) = (1/2)*((diff(diff(_eta[v](u, v), v), v))*u*v^2+(diff(_eta[v](u, v), v))*u*v-4*(diff(_xi[u](u, v), v))*v^2-_eta[v](u, v)*u)/(u*v^2), diff(diff(_xi[u](u, v), v), v) = (diff(_xi[u](u, v), v))/v}$

(3)

For the second step, use DEtools[initialdata]

>

$T := DEtools[initialdata]({diff(diff(diff(_eta[v](u, v), u), v), v) = (-(diff(diff(_eta[v](u, v), u), v))*v+diff(_eta[v](u, v), u))/v^2, diff(diff(diff(_eta[v](u, v), v), v), v) = (3*(diff(_eta[v](u, v), v))*v-3*_eta[v](u, v))/v^3, diff(diff(_eta[v](u, v), u), u) = 2*(diff(_eta[v](u, v), u))/u, diff(diff(_xi[u](u, v), u), u) = (2*(diff(diff(_eta[v](u, v), u), v))*u^2*v+2*u^2*(diff(_eta[v](u, v), u))-2*v*(u*(diff(_xi[u](u, v), u))-_xi[u](u, v)))/(u^2*v), diff(diff(_xi[u](u, v), u), v) = (1/2)*((diff(diff(_eta[v](u, v), v), v))*u*v^2+(diff(_eta[v](u, v), v))*u*v-4*(diff(_xi[u](u, v), v))*v^2-_eta[v](u, v)*u)/(u*v^2), diff(diff(_xi[u](u, v), v), v) = (diff(_xi[u](u, v), v))/v})$

No underlying infinite dimensional symmetry group

>

The underlying finite symmetry group is 8-dimensional

>

[_eta[v](u[0], v[0]) = _C1, (D[1](_eta[v]))(u[0], v[0]) = _C2, (D[2](_eta[v]))(u[0], v[0]) = _C3, (D[1, 2](_eta[v]))(u[0], v[0]) = _C4, (D[2, 2](_eta[v]))(u[0], v[0]) = _C5, _xi[u](u[0], v[0]) = _C6, (D[1](_xi[u]))(u[0], v[0]) = _C7, (D[2](_xi[u]))(u[0], v[0]) = _C8]

(5)

>

Download Find_dimension_of_underlying_symmetry_group.mw

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

Something wrong in your formulation?...

Answered: ecterrab 14702

November 21 2018

2 0

Hi guru

Copy and paste is not convenient. It is prone to errors and extra work for whoever would like to get involved with your computation. So next time could you please just use the green arrow you see when you prepare your post and attach a worksheet with your problem?

In the meantime, at the end I am posting what I could understood of the pasted lines you posted: the tensor you define is not identically zero. Regarding tensorial simplification, you could give a look at the help page of Physics:-Setup, the section on tensorsimplifier. I paste here the section of that help page for convenience. You set is as in Setup(tensorsimplifier= your_simplifier).

tensorsimplifier
Any procedure to be automatically applied when tensor components are computed (e.g. for the general relativity tensors)
The default tensor simplifier, automatically applied when computing the components of the predefined general relativity tensors, and also of any user-defined tensor, is Physics:-TensorSimplifier, a general simplifier withemphasisin handling radicals. Depending on the problem, however, other kinds of simplification may be more convenient. When the tensor components involve large algebraic expressions, for speed reasons, one may also prefer to only apply a (fast) normalization - for this purpose use tensorsimplifier= normal (see normal). One can also set tensorsimplifier= none in which case no simplification is applied but for some unavoidable zero recognitions performed in a few intermediate steps (e.g. when you set a spacetime metric, to verify that its determinant is different from zero). To restore the tensor simplifier to its default value use tensorsimplifier= default or Setup(redo, tensorsimplifier).

And the following is what I understood, copy and pasted, of what you posted

First set the dimension and the coordinates

>

restart; with(Physics); Setup(dimension = 3, coordinates = (X = [x, y, t]), mathematicalnotation = true)

$`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x, y, t)}$

(1)

Now set the values of ut, ux and uy entering the metric

>

ut := Physics:-diff(u(X), t); ux := diff(u(X), x); uy := diff(u(X), y)

(2)

Use a compact display to see things more conveniently

>

(3)

This is the line element copied from your post

>

(4)

Is the above what you intended to enter? See if there is not a typographical mistake around ... Putting all in a single line to be executed makes difficult to spot handmade written typos.

Assuming there are no typos, this is the metric

>

$[metric = {(1, 1) = -(diff(u(X), t))^2, (1, 3) = (diff(u(X), x))*(diff(u(X), t)), (2, 2) = (diff(u(X), t))^2, (2, 3) = (diff(u(X), y))*(diff(u(X), t)), (3, 3) = -(diff(u(X), x))^2-(diff(u(X), y))^2+1}]$

(5)

>

Physics:-g_[mu, nu] = Matrix(%id = 18446744078287601782)

(6)

Note that in the above you have derivatives, just displayed indexed (compactly) for convenience. To see what is behind you can always input show

>

Physics:-g_[mu, nu] = Matrix(%id = 18446744078287601782)

(7)

Now, in your post you use a letter d, but you do not indicate its value. Does it represent the dimension? Assuming that is the case, I set it here to 3

>

(8)

The tensor your define (you can, but you don't need to indicate which indices are contravariant)

>

S[mu, nu] = Physics:-Ricci[mu, nu]-(1/4)*Physics:-Ricci[`~alpha`, alpha]*Physics:-g_[mu, nu]

(9)

Is that the tensor you actually intended to define in 3 dimensions?

Moving forward with what you posted, define it now

>

${Physics:-D_[mu], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-Ricci[mu, nu], Physics:-Riemann[mu, nu, alpha, beta], S[mu, nu], Physics:-Weyl[mu, nu, alpha, beta], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-Christoffel[mu, nu, alpha], Physics:-Einstein[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(10)

Next what would be the Cotton tensor for this metric, if everything above is correctly defined

>

(11)

>

${C[mu, nu, rho], Physics:-D_[mu], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-Ricci[mu, nu], Physics:-Riemann[mu, nu, alpha, beta], S[mu, nu], Physics:-Weyl[mu, nu, alpha, beta], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-Christoffel[mu, nu, alpha], Physics:-Einstein[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(12)

We know at this point that does not return the empty set, indicating there are various nonzero components, that as you say they are large in size (although that is a red-herring here, the problem is that they are not zero).

Get the indices of the components different from zero

>

(13)

Sort them by length, to inspect the smaller one

>

[[1, 1, 2] = 43528, [1, 2, 1] = 43528, [2, 1, 2] = 45955, [2, 2, 1] = 45955, [3, 1, 2] = 66528, [3, 2, 1] = 66528, [2, 1, 3] = 75924, [2, 3, 1] = 75924, [1, 1, 3] = 77652, [1, 3, 1] = 77652, [2, 2, 3] = 80613, [2, 3, 2] = 80613, [1, 2, 3] = 81096, [1, 3, 2] = 81096, [3, 1, 3] = 126082, [3, 3, 1] = 126082, [3, 2, 3] = 130258, [3, 3, 2] = 130258]

(14)

So is the smallest one, of length 43528 of whatever units. Check its length after simplifying with simplify (that nowadays uses simplify/size by default)

>

(15)

OK, that is readable. Check it out:

>

(16)

It is one page, and no radicals nor special functions, this is just a differential polynomial, and clearly not zero. If you were expecting zero, I'd say there is something wrong in your formulation, not related to simplification of tensors.

>

Download Cotton_tensor_and_simplification.mw

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

Fixed within the Physics Updates version...

Answered: ecterrab 14702

November 19 2018

4 0

Thanks for pointing at this one, nm, there was indeed a typo in new code for tackling PDE & BC, it is fixed installing the Maplesoft Physics Updates version 208 (or higher). After installing the fix you get

>

pde := diff(u(r, theta), `$`(r, 2))+(diff(u(r, theta), r))/r+(diff(u(r, theta), `$`(theta, 2)))/r^2 = 0; bc := u(r, 0) = 0, u(r, Pi) = 0, u(0, theta) = 0, u(1, theta) = f(theta); sol := pdsolve([pde, bc], u(r, theta), HINT = boundedseries(r = 0))

diff(diff(u(r, theta), r), r)+(diff(u(r, theta), r))/r+(diff(diff(u(r, theta), theta), theta))/r^2 = 0

* trying method "_Fn" for 2nd order PDEs
   -> trying "linear_in_xt"
   -> trying "BC_equal_0"
* trying method "_Cn_cn" for 2nd order PDEs
* trying method "Wave" for 2nd order PDEs
   -> trying "Cauchy"
   -> trying "SemiInfiniteDomain"
   -> trying "WithSourceTerm"
* trying method "Heat" for 2nd order PDEs
   -> trying "SemiInfiniteDomain"
   -> trying "WithSourceTerm"
* trying method "Series" for 2nd order PDEs
   -> trying "ThreeBCsincos"
   -> trying "FourBC"

<- trying "FourBC" successful
<- method "Series" for 2nd order PDEs successful

u(r, theta) = Sum(2*(Int(sin(n*theta)*f(theta), theta = 0 .. Pi))*r^n*sin(n*theta)/Pi, n = 1 .. infinity)

(1)

>

Download Fixed_in_version_208.mw

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

Partial information....

Answered: ecterrab 14702

November 10 2018

4 2

Hi

There is partial information. There are the two Mapleprimes posts, Maple 2018: Updates to Physics Differential Equations and Mathematical Functions and Tensor Product of Quantum State Spaces. There are also several answers I gave in this forum that have the word "Fixed" in the title (you can give a quick look at these clicking my name in this answer - a page with a summary of my participation in this forum will open - and there click on "Answers").

As a summary, the current version of the Maplesoft Physics updates for 2018 (version 193), actually means quite more than 193 changes posterior to the release of Maple 2018, divided into three categories:

Fixes and adjustments all around, in code that is relevant to Physics, Differential Equations and Mathematical Functions.
Significant developments in the computation of exact solutions for PDE & Boundary Conditions problems - some of these posted here, see for instance Solving PDEs with initial and boundary conditions: Sturm-Liouville problem with RootOf eigenvalues.
Significant developments in the quantum part of Physics, mainly several improvements in the handling of Dirac's notation that allowed for the introduction of tensor products of quantum states in a much more general way, including setting disjointed Hilbert spaces using Setup, also a full implementation of coherent states, including their typesetting, a myriad of improvements in the normalization of expressions involving quantum operators, Bras and Kets (using Physics:-Normal) and in the handling of commutation rules, including those for the Pauli matrices.

Anyway the information publically available is incomplete, I didn't have the time to present the improvements in a more complete and organized manner. That typically happens in the "What's new in Physics" help page of each Maple release, whose contents summarizes the changes of the whole year and I frequently post here in Mapleprimes before the release is out.

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

casesplit and pdsolve OK...

Answered: ecterrab 14702

November 08 2018

3 0

casesplit_and_pdsolve_ok.mw

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

Yes....

Answered: ecterrab 14702

November 07 2018

2 5

Hi Christopher,

Note first that the Maplesoft R&D Physics webpage has the Physics Updates for the previous releases Maple 2017, Maple 2016 and Maple 2015 - only the latest one for each of them. This webpage was cleaned-up removing updates for some older releases.

Not exactly what you asked but, regarding maple 2018, the first release that has updates distributed through the Maple cloud, if you 'view' the package you see the instructions to install any previous version of the Physics Updates for Maple 2018. Being that we are at version 192, that means you have an archive of 191 previous versions. This repository may remain available as such when Maple 2019 becomes the current release next year.

On the versions for Maple 2018, additionally, not mentioned in that 'view' of the package's update, a few updates ago I introduced the following: Physics:-Version, that tells you the version on the cloud and in your computer so that you can see whether you have the latest version, now also installs any version. For example, if you have the latest update, input Physics:-Version(123) and you will have version 123 installed (and remember that in version 123 Physics:-Version does not have this capability of installing the package).

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

How to set those algebra rules....

Answered: ecterrab 14702

November 07 2018

4 7

Hi,

First of all, assuming you are using Maple 2018, be sure you have installed the free upgrade to Maple 2018.2 and also have the latest Maplesoft Physics Updates (version 192 or higher) installed in order to reproduce what is shown below.

>

The following is what you entered first, and indicates that A and C act on the same space, then B and C act on the same space, but A and B do not act on the same space - hence A and B commute, but not A and C or B and C. All bases are discrete with dimensions Na, Nb and Na Nb

>

Regarding your first question: indicating the dimensions of A and B does not determine the dimension of C, so indeed you need to tell the system what is C's dimension, if you are going to use that (it mainly serves the purpose of computing projectors and their use), not otherwise.

About your intention of creating a bracket rule such that you cannot define a bracket rule of this sort (two Bras times one Ket, that is not really a Bracket) but you can define single Kets that belong to C and that have two quantum numbers, ie representing a tensor product, and you can assign dimensions to each of the quantum numbers as you wish. Quoting from the help page for Setup,

"It is valid to state different dimensions for different quantum numbers of Kets of a single basis. For that purpose, if the label of the basis is A, you can set the dimension of each quantum number entering , where and are positive integers, algebraic expressions representing them, or ranges of the form . This dimension of a quantum basis is used to construct projectors when you call the Projector command."

For example, add another quantum space label, say F, and set the dimensions accordingly, noting that your dependence on t is a continuous dependence (in your post I see it as a function, not as an index)

>

[disjointedspaces = {{A, C, F}, {B, C, F}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C[1] = Na, C[2] = Nb}, quantumcontinuousbasis = {F}]

So your bases look like this

>

`&Iopf;__A` := Projector(Ket(A, i)); `&Iopf;__B` := Projector(Ket(B, i)); `&Iopf;__C` := Projector(Ket(C, i, j)); `&Iopf;__F` := Projector(Ket(F, t))

Sum(Physics:-`*`(Physics:-Ket(A, i), Physics:-Bra(A, i)), i = 1 .. Na)

Sum(Physics:-`*`(Physics:-Ket(B, i), Physics:-Bra(B, i)), i = 1 .. Nb)

Sum(Sum(Physics:-`*`(Physics:-Ket(C, i, j), Physics:-Bra(C, i, j)), i = 0 .. Na-1), j = 0 .. Nb-1)

Int(Physics:-`*`(Physics:-Ket(F, t), Physics:-Bra(F, t)), t = -infinity .. infinity)

For instance,

>

From you post I understand that your bracket rule would then be

>

Now you have

>

And with that,

>

Int(X[a, b](t)*Physics:-Bra(F, t), t = -infinity .. infinity)

This answers the question on how to do what I understood you were trying to do. Note next that you can set some rules that have to do with C states being tensor products of A and B states, For example, if

>

Then the bracket rules would be

>

Set these rules

>

Now you have

>

And hence

>

Sum(Physics:-`*`(Physics:-Ket(B, j), Physics:-Bra(C, n, j)), j = 0 .. Nb-1)

>

Sum(Physics:-`*`(Physics:-Ket(A, i), Physics:-Bra(C, i, n)), i = 0 .. Na-1)

If you tell how would A and B Bras contract with F Kets that can also be implemented as a bracket rule, after which you can use them and Simplify will take them into account when simplifying expressions. Without these rules the system doesn't know how to compute these other ones

>

Int(Physics:-Bracket(Physics:-Bra(A, n), Physics:-Ket(F, t))*Physics:-Bra(F, t), t = -infinity .. infinity)

>

Int(Physics:-Bracket(Physics:-Bra(B, n), Physics:-Ket(F, t))*Physics:-Bra(F, t), t = -infinity .. infinity)

I'm not sure I interpreted your question correctly. If the above does not answer your question I'd need more details on the problem you are trying to formulate in order to suggest you something else.

>

Download algebra_rules_(reviewed).mw

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

Solved....

Answered: ecterrab 14702

November 06 2018

6 4

Hi

This problem, that can be considered as one with discontinuous boundary conditions (see my previous reply pointing at their classical incompatibility) is now solved.

>

u(x, y) = ((exp(2*Pi)-1)*(Sum((-1)^n*n*(exp(2*Pi)-1)*exp(n*(Pi-y)-Pi)*sin(n*x)*(exp(2*n*y)-1)/(Pi*(n^2+1)*(exp(2*Pi*n)-1)), n = 1 .. infinity))+(exp(2*Pi)-1)*(Sum(2*sin(n*y)*exp(n*(Pi-x))*n*sinh(Pi)*((-1)^n+1)*(exp(2*n*x)-1)/(Pi*(exp(2*Pi*n)-1)*(n^2-1)), n = 2 .. infinity))+sin(x)*(-exp(y)+exp(-y+2*Pi)))/(exp(2*Pi)-1)

(1)

The improvement is available to everybody within the Maplesoft Physics Updates version 190 or higher. (Note that since its version 188 the Physics Updates requires Maple 2018.2, the free upgrade for those having Maple 2018.)

Actually, there is a large number of improvements in exact solutions to PDE & BC problems. I mentioned one in a previous post on Sturm-Liouville problems with RootOf eigenvalues. I will try to summarize next week the new types of problems that can now be solved in maple 2018.2 and beyond.

Download weak_solution_-_problem_with_discontinuous_boundary_conditions.mw

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

Physics:-Define...

Answered: ecterrab 14702

November 02 2018

3 0

Hi; John is correct: besides the most relevant tensors of General Relativity, the idea in Physics is to provide flexible ways for you to define, using Physics :-Define (it is worth looking at its help page), any tensor. That is, in any dimension, even a tensor in spacetime, in only space, or in the tetrad system of references (for that purpose pass the corresponding indices in the definition sent to Define). That, of course, allows you for defining not just the Cotton tensor but any tensor that makes sense in your formulation or intermediate computations.

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

Fixed in the Physics Updates version 172...

Answered: ecterrab 14702

November 01 2018

4 1

Hi

This problem was one in MultiSet, not in DifferentialGeometry. Anyway, it is fixed now, and the fix uploaded for everybody, available within the Maplesoft Physics Updates version 172 or higher. With the Updates installed, you get

Download error_(reviewed).mw

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

look closer at your metric ......

Answered: ecterrab 14702

October 23 2018

3 1

Hi,

Your coordinates are [x, y, z, t], and the line element of your metric is 4*dx*dt-dy^2-dz^2+4*u*(dt^2)). Look closer ... the line elements does not contain the coordinates. Therefore all the derivatives of the metric with respect to the coordinates are equal to zero, so all the Christoffel symbols (proportional to those derivatives) too, and with it, all of the Ricci, Riemman and Weyl tensors are equal to 0.

In the UPDATE I read that u is a function of the variables (not specified ... I imagine you meant to say coordinates x,y,z,t?). If that is the case, definitely this is the problem. To answer that question, give it a try, enter change u by u(x,y,z,t) in your input, press enter, and you will see that all the general relativity tensors, starting with Christoffel, now have nonzero components.

And that resolves the issue. Tip: use CompactDisplay for u(X), and you can type u(X), no need to type u(x,y,z,t).

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

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

Ask a Question

Create a Post

14702 Reputation

24 Badges

MaplePrimes Activity

These are answers submitted by ecterrab

J F Ogilvie You have a very p...

Physics Updates version 240....

Solution - not hanging....

Fixed in version 201 of the Maplesoft Ph...

PDEtools:-DeterminingPDE and DEtools[ini...

Something wrong in your formulation?...

Fixed within the Physics Updates version...

Partial information....

casesplit and pdsolve OK...

Yes....

How to set those algebra rules....

Solved....

Physics:-Define...

Fixed in the Physics Updates version 172...

look closer at your metric ......

Save this setting as your default sorting preference?

Ask a Question

Create a Post

Generating PDF…

Save this setting as your default sorting preference?
Note: You can change your preference any time in your account settings
Don't show this again