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MathGroup Archive 2004

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RE: Re: Matrix Expansion question to Mathgroup

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47869] RE: [mg47842] Re: Matrix Expansion question to Mathgroup
  • From: "David Park" <djmp at earthlink.net>
  • Date: Thu, 29 Apr 2004 03:05:38 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Harold,

I'm not certain that simply appending rows or appending columns would be a
legitimate operation in tensor calculus.

In any case, the Tensorial package at my web site has commands that handle
these kind of operations. It allows the CircleTimes notation with slot
arguments for tensors and there is a ConstructDirectProduct command.

Next there are SetTensorValues and SetTensorValueRules commands. These have
an option that allows the user to not only set single values for components,
but to also set array values to components. For example, basis vectors may
be given a list of xyz components for values.

The Help documentation also has a notebook on "Matrices, Arrays and
Tensors". It illustrates the relation between tensor index notation and
working directly with matrices and arrays. The direct product of two tensors
is obtained by using Outer. The more interesting constructions are forming
contractions on arbitrary slots. Tensorial has a command ContractArray that
will do tensorial contraction on a Mathematica style array. (Hartmut Wolf
helped me with the routine.)

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: Harold Noffke [mailto:Harold.Noffke at wpafb.af.mil]
To: mathgroup at smc.vnet.net

Larry:

Your question is not trivial, because what you have is a rank-3
tensor, and I was not able to get AppendRows and AppendColumns to work
for rank-3 tensors A and B in a simple programming example.  It is
obvious that each of your matrix elements are lists, and the only
lists you want affected by AppendRows and AppendColumns are the
outermost two -- i.e., in dimensions 1 and 2.

MathGroup ... Do we have packages available which extend AppendRows
and AppendColumns to tensors?

Regards,
Harold




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