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