1410 Reputation

14 years, 216 days

```--------------------------------------
Mario Lemelin```
```Maple 14.00 Win 7 64 bits
Maple 14.00 Ubuntu 10,04 64 bitsmessagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987```

Calculation of the Euler-Lagrange (or La...

Just to mention that 10 years later, I come accross that simple way to dol it in Maple 2020.  So I was able to do manually the calculation and check with Maple if I was right.  Thank you.

Thank you but ........

Since I will do 3 courses in Quantum Mechanics (MITx), I am wondering if it would be an added bonus to use the physics package?

Thank you again for the fast responses.

I know now how to do it...

With you answer, I found out that what I can do is:

> DifferentialGeometry:-Library:-MetricSearch()

And I can find all the metrics as we can see in the book: Stephani - Exact Solutions of Einstein's Field Equations -Cambridge University

That is great.  Thank you!

You got it...

If I put t := 3 [s], I want to be able to transform it in [m] by using the contextual menu..  But for Maple, this is not possible.  I have to do it manually.  When I load the Physics package, I would like that units take into account that c = 1, etc).

Is this possible or too complex?

This is why I need it for...

When you decide that c=1, because the equations are simpler, this make it problematic for an introduction on general relativity.  So I would like to be able to write an equation like this -t^2+x^2+y^2+z^2 and have the result in meter.  That help to check if your calculation is coherent.  This c=1 has an effect everywhere in the theory and I was albe to see in different instances that it complexify the comprehension for the beginners.

A book on General Relativity by using th...

Thank you for the reference.

Mario

This is a quirk of copy-paste...

Here the real commands:

>Setup(metric = Matrix(3, 3, [[1/(-r^2+1), 0, 0], [0, r^2, 0], [0, 0, r^2*sin(theta)^2]], shape = symmetric))

Isn't that fun!  Having done a course on General Relativity, it help to understand what we are doing.

Mario

Thank you...

Thank you again John for your help on this.  Even if I do it in 4D, I only need to put g[0,0]=1.  But your idea help me do that:

restart;
with(Physics); Setup(mathematicalnotation = true, dimension = 3); Coordinates(X = (r, theta, phi)); Setup(metric = Matrix(3, 3, [[Physics:-`^`(1-Physics:-`^`(r, 2), -1), 0, 0], [0, Physics:-`^`(r, 2), 0], [0, 0, Physics:-`*`(Physics:-`^`(r, 2), Physics:-`^`(sin(theta), 2))]], shape = symmetric));

g_[];
Define(A, B);
Setup(differentiationvariables = X);
seq(Christoffel[j, mu, nu, matrix], j = [`~1`, `~2`, `~3`]);
seq(Ricci[mu, nu, matrix], mu = 1 .. 3);
Ricci[scalar];
Einstein[mu, nu, matrix];

I am starting to manage well the physics package.

Mario

A book on General Relativity by using th...

It would be great to have a book on general relativity with commands, templates for the most used metric and exeamples.  It should take into account that it would need two parts, one for introductory courses and one for advanced users.  I tried to find books like that but with no success.

Congratulations Robert...

You deserve all those thanks that you receive.  For me in particular, I saw on you a mentor for working with Maple.  You were always there when I needed.  So I really hope that your mate will be happy and yourself should feel happy too for all the helps you give to so numerous people who wanted to start with Maple.  And yes, clickable calculus is a big success of yours

Thank you again Robert,

Mario Lemelin

I will do it by hand, since Maple cannot...

First of all, a big thank you for all the work you put on this post.

Secondly, when I wrote the Riemann tensor, I was in an angry mood.  At that point, I had decided to do it by hand, since it took too much effort to do something that it was supposed to be simple in the Physics package.  It is my impression that the package, for the moment, is built to get faster calculation of known metrics.  I think that a function like linearize should be part of the package.  That would help us to test other kind of metric that are not listed in the metric list.

So I will stop working in this because I have other calculations to make.  So thank you again for your help.  Maybe later will I come back to this.

Can this be done...

I am sorry that the new linearize does not work with seconde derivative.  But to do what I need, we can use the definition that we get from

`linearize(Christoffel[~1,2,3]);`

Now, the calculation I want to do is this one, meaning the rhs of it

Can this be done.

Some questions in the response...

First, thank you for this very well explain steps.  The first thing I noticed is that g_[mu,nu] must be equal to eta_[mu,nu]+h[mu,nu].  This is important because eta will be apply on the first derivative.  In fact, I should show you what I want to calculate.

Secondly, I just learn that semi-colon is the covariant derivative while the comma mean the standard partial derivative.  It seems to be somewhat different in books that I read.

And the linearize procedure is very interresting.  So I will play a bit with it and if I ran into problems, I will contact you in this post.

Thanks again,

Mario

It did the job but it does not give the result of the derivative since it is written that the derivative is with respect to 1,2,3,4.  Thank you for very much for your help.

By the way, I forgot to do the derivative of the .  Anyway, I will work with the halp files and thank you again.

Mario Lemelin

Maple 2016 Win 10 x64

But still, I have to check this...

So I need to prove that

is the same (P is the function psi) that if I did this calculation

That is what I need to check.  That is why I ask you how to see explicitly the result of that last equation.  I hope I am explaining myself clearly.

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