Items tagged with metrics

Dear Friends, I work with physics paсkage. I have a quation. I don't understend how one works with metrics. For example, let:

Very good!

1) It doesn't work. Why? (I want exactly gamma_[A,B], rather than g_[A,B], because as i guess gamma_[A,B] has a signature [1,1,1] but g_[A,B] has a signature [-1,-1,-1])

 2) And how may I see what is matrices g_[A, B], gamma_[A, B] explicitly? That is I know how to see what is g_[mu, nu], for this one needs write "g_[];".  But how may I see g_[A, B] and gamma_[A, B] in explicitly forms?

3) Why command Trace(g_[mu, nu]))  does not work?"



I am trying to implement some data-intensive algorithms like: comuting similarity scores, clustering etc. How efficient Maple is in doing these operations? I mean is it comparable to MATLAB in these operations? What toolboxes are useful in these? I am trying to build a recommender system.


I am using Maple18 and not sure if Maple has any advantage in implementing these type of algorithms over MATALB??




I need to find the Killing vectors of a metric.

I initiate the session as

> restart;
> with(DifferentialGeometry); with(Tensor); with(LieAlgebras);
> DGsetup([t, r, z, phi], M);

and enter my metric as

M > g1 := evalDG(-dt &t dt ...);

I do not have an unknown function in my metric but I have two free parameters (e.g. a and b).

I use

M > K1 := KillingVectors(g1, parameters = [a, b]);

What is the distance between the trigonometrical polynomials of the form a0/2+a1*cos(Pi*x)+b1*sin(Pi*x) and the polynomials of  degree at most 1, ie c0+c1*x, in the Chebyshev metrics on the interval [-1,1] and in the L^2 metrics on the same interval?


   There are a lot of Maple applications in calculus,...

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