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Re: Can't quite figure out tensors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96977] Re: Can't quite figure out tensors
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Sat, 28 Feb 2009 06:45:20 -0500 (EST)
  • References: <go8in6$lg2$1@smc.vnet.net>

Aaron Fude wrote:

> Hi,
>
> I'm trying to write code that will produce Christoffel symbols for
> various coordinate systems. I would like to use the definition that
> yields Gamma_ij^k as the partial of the covariant basis e_i with
> respect to variables x^j dotted with the contravariant vector e^k. So
> far I have
>
> z[r_, theta_] := {r Cos[theta], r Sin[theta]}
> ei[r_, theta_] := {Derivative[1, 0][z][r, theta],
>   Derivative[0, 1][z][r, theta]}
> gij[r_, theta_] := ei[r, theta].Transpose[ei[r, theta]]
> gIJ[r_, theta_] := Inverse[gij[r, theta]]
> deidxj[r_, theta_] := {Derivative[1, 0][zi][r, theta],
>   Derivative[0, 1][zi][r, theta]}
>
> and now i need to form the tensor product
> deidxj * gIJ * ei
>
> and it has proven to be a bit to intense for me to pull off. Could
> someone show me how to do that?
>
> Many thanks in advance,
>
> Aaron
>

Hi Aaron,
I made a small package, which is able to calculate the Christoffel
symbols, the curvature tensor and so on from a given set of variables
and a metric tensor.

you can download it from

<http://www.pbreitfeld.de/brfART.m>

Documentation and examples are here:

<http://www.pbreitfeld.de/brfART-Bsp.nb>

usages and examples are in German though

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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