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Can tensor packages do this...

• To: mathgroup at smc.vnet.net
• Subject: [mg112713] Can tensor packages do this...
• From: Sam Takoy <sam.takoy at yahoo.com>
• Date: Tue, 28 Sep 2010 06:03:26 -0400 (EDT)

Hi,

Is there a tensor package that performs symbolic tensor operations. What
I have found so far is packages that, given a tensor expression, will
evaluate it for a particular surfaces. But I am looking for something
else. I can't describe it, but I can give an example.

I'm looking for a package that can start with the LHS of the following
expression and arrive at the RHS:

$N^{i}N^{j}\nabla _{i}\nabla _{j}\psi =\nabla _{i}\nabla ^{i}\psi -\nabla ^{\alpha }\nabla _{\alpha }\psi +B_{\alpha }^{\alpha }N^{i}\nabla _{i}\psi$

N^{i} is the normal, B_{\alpha }^{\alpha } is mean curvature, nabla _{j}
is the covariant derivative on the surface.

Many thanks!

Sam



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