Linked Questions
13 questions linked to/from Contracting with Levi-Civita (totally antisymmetric) tensor
3
votes
3
answers
7k
views
Sum with Levi-Civita [duplicate]
I'm trying to write the expression
$$\sum_{\alpha,\beta = 1}^{4}\epsilon_{\mu \nu\alpha\beta}a^{\nu} b^{\alpha} c^{\beta}$$
in Mathematica, where $\epsilon$ is the Levi-Civita symbol and $a$, $b$, $c$ ...
user18822
3
votes
1
answer
966
views
Explicit Contraction of Tensor Indices [duplicate]
Is there any easy way to explicitly contract indices of several given tensors.
For example,
...
- 950
0
votes
1
answer
972
views
Contracting Levi-Civita [duplicate]
I am trying to contract two Levi-Civita symbols in tensor format like so:
$\epsilon_{a b} \epsilon_{c d}$
This code generates the Levi-Civita:
...
- 316
3
votes
1
answer
866
views
Tensor contraction for two antisymmetric tensors [duplicate]
I have SparseArray for two rank 4 antisymmetric tensors A and B, I want to compute $T_{abef}=\sum_{cd}A_{abcd}B_{efcd}$. How should I do it?
- 687
54
votes
6
answers
46k
views
How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?
I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes,...
- 675
73
votes
5
answers
21k
views
Can Mathematica do symbolic linear algebra?
For instance, is there some way I can say "let A and B be arbitrary real $m\times n$ and $k\times m$ matrices, Simplify[Transpose[Transpose[A].Transpose[B]]]" and ...
- 36.4k
16
votes
3
answers
7k
views
How to declare a 3D vector variable?
How can I do vector calculations without telling Mathematica the vector entries?
I have very many arbitrary linear combinations in $\mathbb{R}^3$ which I want to perform some general calculations on (...
- 345
3
votes
2
answers
4k
views
Using the epsilon tensor in Mathematica
I'm having a great deal of trouble getting started on a weekly homework assignment in Mathematica. The assignment requires we use the epsilon tensor which is apparently built into Mathematica as ...
- 85
3
votes
1
answer
2k
views
Traces of products of Pauli matrices
Given a matrix $M$ of shape $2^L*2^L$, I would like to compute all the traces $\text{Tr}( M.(\sigma^{n_1}\otimes\sigma^{n_2}\otimes\ldots\otimes\sigma^{n_L})) $ for $n_1=1...4$, $n_2=1...4$, ..., $n_{...
- 835
3
votes
2
answers
663
views
Tensor contraction
How do I let mathematica compute a tensor contraction like
$\delta_{ab}\delta_{bc}$
with an output
$\delta_{ac}$
efficiently?
I tried TensorContract and TensorReduce but they were not helpful.
...
- 199
3
votes
1
answer
557
views
5
votes
0
answers
1k
views
Tensor product involving Levi Civita symbol
I'm working with xAct package. I've defined the tensor component values and my issue is that I want an expression involving Levi Civita symbols and tensor components, I don't know how to deal with it. ...
- 243
0
votes
0
answers
691
views
Symbolic tensor product calculation
I am trying to calculate the a symbolic tensor product
$\langle \nabla f\otimes f,\nabla g\otimes g\rangle ^2+(\langle \nabla f\otimes g,\nabla f\otimes g\rangle +\langle \nabla g\otimes f,\nabla g\...
- 411