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MathGroup Archive 2009

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Can't quite figure out tensors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96945] Can't quite figure out tensors
  • From: Aaron Fude <aaronfude at gmail.com>
  • Date: Fri, 27 Feb 2009 06:27:23 -0500 (EST)

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


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