Questions tagged [tensors]
Use this tag for questions that involve tensors. Tensors are fundamental tools for linear computations, generalizing vectors and matrices to higher ranks. Mathematica 9 introduces powerful methods to algebraically manipulate tensors with any rank and symmetry.
321
questions
0
votes
1answer
27 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.
...
0
votes
0answers
41 views
How do I apply assumptions to a table of functions
I have a table, really its a tensor but anyways I would like to apply an assumption to it, i.e. 1 - 2 phi[t,x,y,z] == 1 and have it print the tensor after it has ...
0
votes
0answers
39 views
Use Mathematica to draw a tensor-like network
What are the Mathematica ways to draw this seemly delicate figure? Such that we can output a PDF file in the end.
2
votes
1answer
27 views
xAct working with an unspecified function
I am trying to use xCoba with a diagonal metric depending on an unspecified function f[r], but I get the errors:
CTensor::...
4
votes
2answers
125 views
How to understand the symmetry of MMA's tensor
tensor = {{{2, 9}, {9, 2}}, {{9, 2}, {2, 4}}};
TensorDimensions[tensor]
TensorSymmetry[tensor]
How can I understand the symmetry of the output ...
1
vote
0answers
83 views
3d plot of young's modulus for anisotropic material
can anyone can help me in plotting 3d plot of young's modulus for anisotropic material. For input i have 6*6 stiffness tensor matrix and hydrostatic pressure value.
I am trying with the following ...
1
vote
1answer
40 views
The Matrix formula of this hamilton is different from that found in the paper
I am trying to rewrite the following Hamiltonian in the matrix form, but I get different results. In this article, the Hamiltonian that represents a three-qubit Heisenberg spin chain
and its matrix ...
2
votes
1answer
40 views
Defining a tensor from an expression of other tensors in xAct
There's been a number of people asking how to set a tensor-valued variable in xAct; equivalently, how to define a new tensor from an expression of existing tensors.
For example, a very simple ...
2
votes
1answer
60 views
How to compute functional derivative against vector in xAct, xTensor or xTras?
I want to compute the functional derivative against vectors.
For example, I have an object that looks like this
$R = h_{ijkl}a^i a^j a^k a^l$
I need to compute $\frac{\delta R}{\delta a^p}= 4 h_{...
0
votes
1answer
68 views
How does Indexed work in terms of sparse array
I want to use indexed given that s is an element [0,500] but I am unsure how to write that without getting a format error or a tensor error.
...
0
votes
1answer
33 views
How to make a tensor product into matrix?
TensorProduct[PauliMatrix[1], DiagonalMatrix[{1, 1}]] // TableForm
created a tensor, which could be flatten to table form.
However, how to make the tensor into a ...
2
votes
1answer
70 views
Kretschmann scalar in xTensor and xCoba
How do I calculate the Kretschmann scalar $K=R_{abcd}R^{abcd}$ with xTensor and xCoba? I have found the functions Kretschmann and ...
2
votes
2answers
107 views
Speeding up the evaluation of a product of 64 matrices, each 16x16, which takes 30 minutes
I need to calculate a very large product of matrices, (64 terms, each a 16x16 matrix). Specifically,
...
2
votes
0answers
41 views
Parallelize and tensor calculus
Is it possible to use Parallelize with tensor calculus functions like TensorContract and ...
3
votes
1answer
62 views
Rewriting a large product of 42 (13x13) matrices with MatrixExp
I am trying to perform a product of a large number of terms of the form MaxtrixExp[...], for example, something like this
...
0
votes
1answer
40 views
Trying to find the double dot product of a Rank 4 and Rank 2 tensor
I understand this question has been asked before, or something very similar to what I'm trying to accomplish at the very least, however I didn't understand much of what was happening in the other ...
6
votes
2answers
423 views
Speeding up sums involving 16x16 matrices and 16x16x16x16 antisymmetric tensor
I need to perform the following contraction involving four 16x16 matrices and a tensor $\theta$ that is 16x16x16x16.
...
4
votes
1answer
102 views
TensorContract and TensorProduct problem
I am trying the calculate the Kretschmann scalar $K$ of a metric $$K=R^{abcd}R_{abcd}$$ where $R$ is the Riemann tensor. If I do
...
0
votes
1answer
45 views
How can I take the divergence of a symbolic vector? [duplicate]
I would like to compute expressions that have the following form:
$$\left(\partial_{p_1} - \partial_{p_2}\right)^2 \left(\partial_{p_1} - \partial_{p_2}\right)^2 \frac{(p_1-p_2)\cdot(p_3-p_4)}{p_1^...
1
vote
1answer
55 views
How to work with Levi civita tensor in xAxt?
Is there any command to work with the Levici vita tensor? In fact, I found LeviCivitaTensor, however, in calculations it doesn't seem practical.
see the example:
<...
0
votes
1answer
71 views
How to flatten a tensor product
Say I have a tensor product of four two dimensional spaces
$\Lambda = S\otimes S\otimes S\otimes S$. The basis of $S$ is CB={{1,0},{0,1}} . I generate the ...
3
votes
1answer
47 views
1
vote
0answers
23 views
Derivatives with dummy indices not commutative after 3d derivative?
Recently I've encountered the following issue in xAct.
I've defined the Manifold and tensors in the following manner
Then consider the following expressions.
In the case where there are 2 ...
0
votes
0answers
22 views
Hamiltonian Analysis in xAct: Variation wrt time derivative of fields
I'd like to use the xAct package to perform the Hamiltonian analysis of a complicated action. To that end, it would be useful to introduce a chart and split indices into "temporal" and "spatial" parts....
4
votes
1answer
67 views
Reduce memory cost with three matrices multiplication
My program is eating up all my RAM and the operation is related to 3 matrices multiplication, as the code shown below.
example code:
...
0
votes
1answer
42 views
FromTensor + TensorContract gives unexpected result for a tensor product of vectors and a matrix
I have written a larger code that uses the TensorSimplify package written by Carl Woll for tensor manipulations. The code, however, produces unexpected results, ...
-1
votes
1answer
119 views
Can I numerically solve these equation in Mathematica? [closed]
I have this couple of equations :
$ \partial_\mu \partial^\mu z^i + G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) \partial_\mu z^j \partial^\mu z^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{l}} ) \...
0
votes
0answers
51 views
Solving differential forms equations
I have this couple of equations in differential forms language:
$ \Delta z^i \star {\bf{1}}+ G^{i\bar{p}} (\partial_j G_{k\bar{p}} ) dz^j \wedge \star dz^k + G^{i\bar{j}} (\partial_{\bar{j}} G_{k\bar{...
0
votes
1answer
59 views
How to multiply the elements of each site of tensor products to each other while using symbolic representation?
If I have, say three sites in a symbolic operator which is of the form A = a⊗1⊗c and I want it to act on another operator B = a1⊗b⊗1 in order to find the commutator A.B - B....
0
votes
0answers
27 views
Contracting the KroneckerDelta should bring it back
I would like to define a function
$$V[\phi] = \sum_{1\leq i,j,k,l\leq dim}\lambda_{ijkl} \phi_i\phi_j\phi_k\phi_l, $$
with $\lambda_{ijkl}$ defined by contractions of the type $\delta_{ij}\delta_{kl}$...
2
votes
0answers
75 views
How to remove the Riemann tensor derivatives using Bianchi identity?
For the third-order Lovelock gravity, after varying the Lagrangian versus the metric, I found some derivatives of the Riemann tensor which should not be appeared. How can I remove them? Maybe using ...
4
votes
1answer
47 views
Computing Higher Order Tensor of Variable Rank
The following code takes a vector x of variable length, computes the outer product of the vector with itself to form the matrix $\rho$ of dimension $2^n \times 2^n$....
4
votes
1answer
74 views
How to Creat a Symbolic Rank 4 Symmetric tensor
I would like to create a rank 4 symbolic tensor with this symmetries
(1) C_ijkl = C_jikl
(2) C_ijkl = C_ijlk
(3) C_ijkl = C_klij
is there any way to apply symmetry (3)?
symmetry (1) and (2) can ...
1
vote
1answer
41 views
Higher Order Tensor of Variable Rank
I would like to write a function, that matricizes a higher order tensor according to the following rule:
Let $\mathcal{A} \in \mathbb{C}^{I_{1} \times I_{2} \times \ldots \times I_{N}}$ be a tensor ...
2
votes
1answer
51 views
Independent permutation symmetry of a tensor [Using TensorSymmetry command]
Suppose I have this tensor $A_{ijkl} = \epsilon_{ik} \epsilon_{jl}+\epsilon_{il} \epsilon_{jk}$. Now I want to find all the independent permutation symmetries of the indices of this tensor. The answer ...
2
votes
1answer
73 views
How do I force this simplification?
I am trying to calculate:$$\epsilon_{ijk}n^iM1^j\epsilon^{lmk}n_lM2_m$$
Defining the vectors as:
M1={M1x,M1y,M1z}
M2={M2x,M2y,M2z}
n={nx,ny,nz}
and using
...
1
vote
1answer
86 views
How to define commutative covariant derivatives in xTensor
I'm new with working xAct package and got stuck defining covariant derivatives that commute with each other.
I want to simulate flat space-time. And here is my code
...
3
votes
1answer
52 views
How do I prove this formula with LeviCivitaTensor?
How do I prove that
$$ \epsilon_{ijk}\epsilon^{ijm}=2\delta_k^m ? $$
If I use
...
8
votes
4answers
379 views
How can I automate this tensor computation?
I am doing this work by hand, but it takes a lot of time and I make several calculation errors, so I was thinking to make Mathematica to calculate this for me, but I am stuck at the very beginning.
I ...
4
votes
1answer
100 views
Symbolic multiplication of tensors
I am trying to do symbolic calculations on Pauli Matrix Algebra. I want to find some way of making CircleTimes[a,b] ** CircleTimes[c,d] map to CircleTimes[a.c,b.d] for every a,b,c,d. I would also like ...
6
votes
1answer
146 views
Speeding up tensor contractions and multiplication
Consider a tensor $T\in\mathbb{R}^{N\times N\times N\times M}$ and two vectors $x,y\in\mathbb{R}^N$. I want to compute the $N\times M$ vector defined by $X_{ij}=\operatorname{tr}(x^\top T_{:,:,i,j}y)=\...
0
votes
0answers
33 views
Doubt about tensor producto of two columns vectors
I want to get the tensor product of two columns vectors for example:
a={1,2,3}
b={2,3,1}
psi0 = ArrayFlatten[TensorProduct[a, b]];
The size of psi0 is 3x3 but it ...
0
votes
0answers
46 views
How to compute gauge variation of expression?
Suppose I have a symmetric tensor field $h_{\mu\nu}$
I want to implement somehow the following gauge variation of this tensor field as follows
$\delta h_{\mu\nu} = \nabla_{\mu}\epsilon_{\nu} + \...
1
vote
0answers
33 views
Inverse fuction of TensorExpand
Is there a way in mathematica to factorize/simplify a dot product? I.e. I have something like a.b + a.c (obviously more complicated expressions) and I would like to factorize terms like
...
10
votes
2answers
575 views
Make symbols atomic, without losing their type
So, I'd like to define a matrix M, that does not decompose into it's constituents when I do things like Tr[M], but I also want it's type to be retained.
(By type, ...
1
vote
0answers
56 views
Print 4x4x4x4 tensor as 4x4 matrix of 4x4 matrices [closed]
I'd like to print the LeviCivitaTensor[4] tensor as 4x4 block matrix of 4x4 matrices
The following code works to display the LeviCivitaTensor[3] tensor as a 3x1 vector of 3x3 matrices.
...
0
votes
0answers
82 views
CompiledFunction::ctfa - Argument should be a rank 4 tensor of machine-size real number
Dear Mathematica community,
I got the following error line:
CompiledFunction::ctfa "Argument {<<1>>} at position 1 should be a rank 4 tensor of machine-size real number"
This is my function:...
2
votes
1answer
165 views
xAct, xTensor: How to avoid clash of indices?
Please refer to the picture below. In the first line, I define the angular momentum vector $\vec{L} = \vec{R} \times \vec{P}$ using the Levi-Civita tensor $\epsilon^{i}_{jk}$. The definition relies on ...
3
votes
0answers
59 views
Lie-algebra valued non-abelian differential forms in Mathematica
I am trying to implement wedge product of Lie-algebra valued differential forms in the non-abelian case. Concretely, I am intereste in 1- and 2-forms, that is, $A$ and $F$. Is there a way of doing ...
2
votes
1answer
140 views
Outer (dyadic) product between vectors of the same index in two lists
I have two lists of vectors and I want to take the outer product between elements in the lists of the same index. Using either Outer or TensorProduct works for e.g. the first two indices:
...
