Re: Covariant derivatives of tensors?

• To: mathgroup at smc.vnet.net
• Subject: [mg107460] Re: Covariant derivatives of tensors?
• From: Erik Max Francis <max at alcyone.com>
• Date: Sat, 13 Feb 2010 05:23:08 -0500 (EST)
• References: <hkeard\$t22\$1@smc.vnet.net> <hkrm9u\$m3f\$1@smc.vnet.net>

```dh wrote:
> to accomodate an unknown number of indices, you may dynamically build
> the iteration specification. Here is an example:
>
> multiindex[exp_, vars_, dim_] :=
>   Table[exp, Evaluate[Sequence @@ {#, 1, dim} & /@ vars]]
>
> if you e.g. say:  multiindex[a[i1, i2], {i1, i2}, 2]
> you get: {{a[1, 1], a[1, 2]}, {a[2, 1], a[2, 2]}}

Thanks for your help.  I did in fact come up with a solution which
involved iterating over each permutation of the list of indices
(creating them via Tuples), then performing the (involved) computation
for each permutation (along with the new covariant index), building a
list of rules, and then constructing an empty (higher-dimensional) array
with Nest and Outer, and finally applying the replacements with
ReplacePart.  This is probably not ideal in terms of efficiency, but it
works.

Since the main excuse here was to 1. get more experience with
Mathematica just for the fun of it, 2. help solidify my knowledge of
tensor calculus, and 3. write a package for the first time, I'll put
together some "examples" using the package and then post it somewhere
for feedback.

--
Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Love is a hole in the heart.
-- Ben Hecht

```

• Prev by Date: Re: Random number with custom distribution
• Next by Date: Re: Re: Normality test
• Previous by thread: Re: Covariant derivatives of tensors?
• Next by thread: Inserting a position-limited Locator inside a Manipulate multiplot