RE: 2 Simple Mathematica Questions. (regarding tensors and matrices)
- To: mathgroup at smc.vnet.net
- Subject: [mg45118] RE: [mg45083] 2 Simple Mathematica Questions. (regarding tensors and matrices)
- From: "David Park" <djmp at earthlink.net>
- Date: Wed, 17 Dec 2003 07:54:34 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Ashok,
For your first question you should use the Outer command.
Amat = Array[A, {3, 3}];
Mmat = Array[M, {3, 3}];
Hmat = Outer[Times, Amat, Mmat];
Hmat[[1, 2, 3, 3]]
A[1, 2] M[3, 3]
On your second question, unfortunately you have to use a different name on
the left hand side to avoid a rucursive definition.
If you wish to try the Tensorial package at my web site I think you might
find a more natural approach to these problems. It has an easy way of
assigning tensor values and using index notation. You wouldn't have to make
an Amat or Bmat matrix because there is already an index notation.
Needs["TensorCalculus3`Tensorial`"]
DefineTensorShortcuts[{{A, M}, 2}, {H, 4}]
That creates tensor shortcuts for second rank A and M tensors and 4th rank H
tensors. With tensor shortcuts defined, we can enter, say, an A tensor with
two up indices as Auu[i,j], or with up and down indices as Aud[i,j] etc.
You could enter the tensor product of A and M, and then expand it to a full
array by the following statements...
Auu[i, j]Muu[k, l]
% // EinsteinArray[]
EinsteinArray expands on the free indices in the expression. You could
obtain a specific element with
Auu[1, 2]Muu[3, 3]
You could set values for the H tensor with
SetTensorValues[Huuuu[i, j, k, l], Auu[i, j]Muu[k, l] // EinsteinArray[]]
and then obtain the same value as above with
Huuuu[1, 2, 3, 3]
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Ashok. R [mailto:ashokr at alum.dartmouth.org]
To: mathgroup at smc.vnet.net
Greetings.
This is my first question:
I am trying to form a 4-tensor, H, whose (i,j,k,l) components are given by
H(i,j,k,l) = M(i,j)A(k,l) where M and A are 2-Tensors (Matrices). This is
what I have been doing so far:
L1 = Array[M, {3, 3}]
L2 = Array[A,{3,3}]
H = Table[L1[i,j]*L2[k,l] {i,3},{j,3},{k,3},{l,3}]
The last statement gives a long output, but not the the correct result. I
want to be able to say
H[[1,3,2,1]] and get M[1,3]A[2,1] as output.
Can someone familiar with tensor manipulation in Mathematica tell me how to
do this ?
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This is my second question:
I want to assign a matrix, A, that has three rows and three columns and each
element is identified by A[i,j]
L1 = Array[A,{3,3}] works, but the array is called L and not A. I tried
A = Array[A,{3,3}] and that, as expected, gave me a warning about
recursions.
Thank you for your assistance. I wish you a pleasant day.
Ashok