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Re: Covariant derivatives of tensors?

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  • Subject: [mg107253] Re: Covariant derivatives of tensors?
  • From: magma <maderri2 at>
  • Date: Sun, 7 Feb 2010 06:11:01 -0500 (EST)
  • References: <hkeard$t22$>

On Feb 4, 12:25 pm, Erik Max Francis <m... at> wrote:
> Working on my tensor library, I'm trying to implement the covariant
> derivative for an arbitrary-rank tensor.  I'm keeping track of which
> indices are contravariant/upper and covariant/lower, so the problem
> isn't managing what each term would be, but rather I'm having difficulty
> seeing how to take an arbitrary tensor and "add" a new index to it.
> This in effect requires running Table with an arbitrary number of
> indices, and then adding one.  Given the arbitrariness of the
> multidimensional array, I'm not seeing how to do it.  The naive approac=
> would be something like:
>         Table[
>             <complex function involving many terms of a[[i1]]=
>         {j, n}, {i1, n}, {i2, n}, ... {ir, n}]
> where the variable si1 .. ir (r of them) range over the value 1 through
> n for each of the indices of the tensor (of rank r), j is the additional
> index added by the covariant derivative, and n is the dimensionality of
> the space.
> I'm not seeing how to do this dynamically, since I don't know in advance
> what the rank of the tensor is, and I'm still relatively new to
> Mathematica.  Any ideas?
> --
> Erik Max Francis && m... at &&
>   San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
>    All the people in my neighborhood turn around and get mad and sing
>     -- Public Enemy

There are excellent tensor packages for Mathematica, which can do this and
much much more.
Tensorial by David Park is low cost.
xAct is free
Check on google or on mathgroup for the links.

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