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

@John Fredsted 

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.

@John Fredsted 

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.

Thanks again for your help

@John Fredsted 

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

@John Fredsted 

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

@John Fredsted 

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.

@John Fredsted 

The input should be:

>`ℏ`

Your solution is perfect.  Since it must be equal to 0, that solve the problem of the exponential. 

But how to ask Maple to explicitely do the second part of the calculation?  I mean to force it to show the partial derivative of Psi(X) so I can confront it with my result.

I am learning a lot and I thank you for this.

I have done the calculation.  Now I want to check if this calculation is the same as the one I obtain after calculating the limit hbar -> 0.  So I need to do this:

>eq1:=g_[`~mu`, `~nu`]*d_[mu]*F*d_[nu]*F

where F is the exponential function exp(I (r,t)/h).  When I do the Check(eq1,all), it said that "The products in the given expression check ok.".

Now, I want to see the result of that calculation but I cannot find the information I need in the help pages.

What should I do?

Again, thank you for your help.

--------------------------------------
Mario Lemelin

Maple 2016 Win 10 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

Thank you very much for this fast way to setup the metric. But what about theta and phi since I choose a time and a plane?

--------------------------------------
Mario Lemelin

Maple 2016 Win 10 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

@Christopher2222 

Thank you again!  Now I will be better equipped for the next course where I will have to manipulate more data.

@Christopher2222 

Thank you for that result.

@Markiyan Hirnyk 

not a lot.  I never really study data analysis.  For example, we see that there is an oscillation with a long period that move the data like a sine wave.  The idea is to find that equation so I can remove it from that data so I will have the small oscillations an a straight line.  Then I suppose that we must use a Fourier's series like sum(a[i]*sin(...)+b[i]*cos(...).

It seems to be more easy if you have Matlab, which I have (R2015b) but I see that this version will be available only from Maple 2016 and that I will have to buy Simulink.  So befor buy this suppplemental product, can it be done in Maple alone?

Thank you for your help Markiam.

After thinking about it, there should be more than two sin waves in this problem.

I have attach her a document for a very simple calculation.  If I want to resolved the problem with tensor, how should I do it.

DirectProductofTensors.mw

I know that I have to do this:

restart:with(Physics):with(DifferentialGeometry):

and some Setup(coordinates( )).

Plese keep in mind I am only beginning with this package.

 Juste added:  Another problem I would like to do:

DirectChangeof_Base.mw

--------------------------------------
Mario Lemelin

Maple 2015 Ubuntu 14.04 - 64 bits
Maple 2015 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

@acer I now have the name of the book that they use.  And it is clear that it is lbf.  So again, thank you for your quick answers.  I am always wondering why do they stick to FPS?