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