@acer The functional P(z) is very practicle and so simple.  Thank you for the idea.  I have a worksheet with an example.Convert_to_exp.mw

@Carl Love Thank you for telling me what it is called. Now I know. At least I knew that Iterator was probably where the solution was. I love that last solution. She taught me a lot about using Maple. Thank you very much.

In readingt a book on diferential forms (Fortney - A Visual Introduction to Differential Forms and Calculus on Manifolds), I stumble on a lot of definitions that I never saw. And another one is what it is called in the book page 94:

At page 94, it is stated the definitiion of the wegde product (See Shuffle.png)

I know about the finite symmetric group Sn. But it's the way the author uses the (k,l)-shuffle, the symbol v sigma (k+l), etc. Does someone can explain this to me and is there a way to do it in Maple so I can multiply the right terms. If you have the book, pages 95-97 is full of symbols of permutation sigma. I get the feeling of what I have to do but I would prefer to better understand it. Or maybe this is not the place for this. In that case, my apology.

Thank you both acer and mmcdara for your solutions.

I don't have to do that with a lot of elements in both sets so performance is not a question. The answer is exactly what I need. And by looking at the solution, it is clear that I would not have been able to solve it by myself. Once again, the pertinence of MaplePrimes has been shown.

Thank you!

@rlopez  Thank you very much Robert for the clarification. It is clear that I will be registered for your webinars. It’s a nice, very appropriate coincidence that your webinar will be about the Differential Geometry package.

I would like to take the opportunity to ask you if you could suggest me some good books on the subject. I can't wait to see the connection with tensors, general relativity and quantum field theory. I send you my best regards. Mario

@acer Thank you. I love the second one. Interresting to see that something so simple by hand becomes more complex on the computer.

Very interresting ways of doing it.

Many times I feel that my plots would be better if it were possible to change the default for the color of the grid. This is, for me, very evident in the examples that you have shown above. When you want to have two 3D plots on the same plot, of course. But even if there is only one plot.

I would add that I would very appreciate if, for a 3D plot, it was possible to create this kind of grids in the background of the plot (not the plot as is). We only have those options: boxed, normal, frame, or none. We could call it "3Dgrid".

What do you think of all this?

@acer  I use the first one. I corrected the "gridlines=[spacing(30,0)" for (3,0) and the x-axis goes from, 0..9. And I get this beautiful plot.

As you can see, on my computer, I see only one color of light gray (except for the principal aces).

Thank you very much for your patience.

Mario

@acer So I upload my document.

Espace-temps_de_Minkowski.mw

I took your advice for the Unit(s). The last thing to be adjusted is as follows. What I need is to have the light-gray gridline on the x-axis to be only on the values of 3, 6 and 9. Not on the 1, 2, 4, 5, etc. This plot will serve as the base for the rest of the work while I will be adding new plot to it.

Thank you for your patience.

Mario

@acer YYou are always a very good help in MaplePrimes. Very appreciated. But there is just one last little detail that I am trying to adjust. If you look at the plot that you have made possible:

The principal tick mark for the x-axis should be on 3, 6 and 9. It is important because I want the principal tick marks on both axes to give the sense that they form cubes. So after one second, the light will be at the point (3,1).

As you must have realized, I am creating a document (in French) for the introduction of the Minkowski diagram of spacetime starting with a Newtonian path–time diagram. And gradually adding the multiple spaceships. Then I will superimpose the axes t prime and x prime on it and show why they are at an angle and what that angle mean.

I am trying to get it right by reading the help but I don't get what I want. Sorry to bother you with that.

Mario

@acer Excellent solutions! That is the first time I see the InertForm use that way. Thank you for your answer. I choose this one:

labels = [x*InertForm:-Display(10)^8*Unit(m), `t `(s)]

that give the right outplut. Is there a way to put the the unit of meter inside a ( ).

I forgot to ask you one more thing. As you can see, the horizontal axis was with 3, 6 and 9. Could you show me how to fix that so that plot always show that, even if I zoom the plot?

Again, thank you acer!

Mario

I tried the document without the ToInert and only using CompactDisplay like this:

>CompactDisplay((v, lambda)(r, t))

And the result of a double derivative is clearly displayed:

So I will go with that. Here the newer version of the file

General_metric_corrected.mw.

Thank you to all that help me.

Mario

@Christopher2222 Your use of ToInert is very interesting. I have used it and it worked, almost correctly. When calculating the Einstein's tensor, there is the elements G[3,3] and G[4,4] where the second derivative of both function does not show the aliases. I wonder if it would work if we were to use the formula R[mu,nu]-1/2*R*g[mu,nu]. Unfortunatly, I don't know how to do that in Maple. I get error all the time.

You will find the new corrected document here.General_metric_corrected.mw

I agree that it would be nice if the CompactDisplay could work for multivariables. Hoping that ecterrab will see this.

Thank you everybody for your help

@Hullzie16 ... but you need to interpret things.. For example, exp(- lamkbda * Lambda) = exp( - lambda) and (lambda * Lambda dot) to lambda dot. Anyway, thank you for that.