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.
351
questions
2
votes
0answers
24 views
How to define tensors similar to Riemann tensor in xAct xTensor xTras
I'm working on a project where we deal with objects very similar to Riemann tensor. In fact they are Christoffel symbols for higher spins. I'm using xTras for modeling problems in wolfram mathematica. ...
12
votes
4answers
720 views
How to rewrite a tensor as a matrix
I put
{TensorProduct[{1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}]}/Sqrt[2]//MatrixForm
and I got
$$
\left(
\begin{array}{cc}
\left(
\begin{array}{cc}
\left(
\begin{...
5
votes
1answer
127 views
Derivative of real antisymmetric matrix in mathematica
Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
3
votes
0answers
40 views
Contracted indices can be interchanged? [migrated]
I am trying to do some research in Lorentz transformations and I get a tensor of the form
$$M_{abcd}=\epsilon_{ab\mu \nu}\Lambda^\mu\hspace{0.1cm}_c\Lambda^\nu\hspace{0.1cm}_d$$
Where $\epsilon_{ab\mu ...
2
votes
1answer
43 views
Fancy Indexing of a 4D array (tensor)
I'm trying to mimic the CoefficientArrays function, which I can't get to work for my symbolic equations. The CoefficientList ...
3
votes
2answers
105 views
Klein-Gordon Equation: how can I write the summation?
I would like to write a program that gives me the Klein Gordon Equations given a metric. I will explain.
My code is in the following:
I) Standard Quantities
I have no doubt here the first part is ...
7
votes
2answers
235 views
How is Grad defined for array particularly in non-Cartesian coordinates?
This question can be viewed as a follow-up of
What is the definition of Curl in Mathematica?
First argument of Grad can be an array, but what definition does ...
0
votes
1answer
32 views
Building an array of T NxM matrices where one item in each matrix changes
As I do not use Mathematica often enough, I am a bit rusty. I need to work on an array of T matrices and each of those NxM matrices has the following pattern:
$$
\begin{equation}
A(t):=
\left(
...
1
vote
1answer
61 views
Tensorial functions
I need to solve a system of ODEs for a function that has a complicated tensorial structure. I believe that NDSolve can deal with this scenario since version 9. Yet, ...
2
votes
1answer
70 views
How to identify specific Christoffel symbols and Riemann Tensor components from a general solution [closed]
I want to learn how to identify specific Christoffel Symbols and Riemman Tensor components from the general solution provided by Mathematica. Let us work out an example to see what I mean clearly.
...
4
votes
1answer
112 views
Computing Christoffel symbols of the second kind [duplicate]
I want to compute the Christoffel-symbol for a given metric. I am using the code here, but I am missing something.
The Chrisfoffel-symbol formula is
$\Gamma^{\mu}_{\phantom{\mu}\nu\sigma}=\frac{1}{2}g^...
2
votes
1answer
61 views
Best way to work with Tensor Networks
I have to write a script in which I have to work with a very simple tensor network but I can't find a nice scalable way to make this work.
The basic object I am working with is a tensor more or less ...
1
vote
0answers
54 views
LeviCivitaTensor contraction indices
My computer has problems when I try to perform a calculation with TensorContract.
In particular, with the second answer to my previous question Contracting indices ...
2
votes
0answers
26 views
Optimising tensor operations under memory constraints
Let riem is a free variable with riem ā Arrays[{4, 4, 4, 4} as assumption. Let:
...
6
votes
2answers
178 views
Contracting indices in lists
Using an answer to this question (Working with Dirac Gamma Matrices using FeynCalc - A simple problem), I defined
...
2
votes
1answer
58 views
Expanding Determinant as Multilinear Alternating Function
I am working with the expression
$$\det\big{|}f(-kx), f(-(k-1)x),\cdots,f(0),\cdots, f((k-1)x), f(kx), g(x)\big{|},$$
where $f,g\colon\mathbb{R}\mapsto \mathbb{R}^{2k+2}$, and want to use the Taylor ...
0
votes
0answers
46 views
Does Solve work with symbolic tensors?
I am considering the usefulness of Mathematica's symbolic tensors to handle algebra which I encounter in acoustics of solids. Is there a way to solve equations written in symbolic tensors? This is ...
2
votes
1answer
31 views
How to state nontrivial tensor symmetry assumptions?
For example dddg, the third derivative of the metric tensor, in dimension $4$.
I need to state that it is symmetric in the first two indices and symmetric in the ...
0
votes
1answer
27 views
Hypothetical aplication of rules/restricting rules to a given context?
I have the code TensorDimensions[TensorContract[c, {{1, 2}}]]. It is in normal form. But if I add the rules:
...
0
votes
1answer
48 views
Correct syntax for tensor operators?
So I have an operator $A_0$ whose matrix representation is given by $$A_0 = \begin{pmatrix} 0 & -i \\ -i & 0\end{pmatrix},$$ and I also have two vector states $|0\rangle$ and $|1\rangle$ ...
4
votes
1answer
167 views
Fourth Order Tensor rotation [duplicate]
What is the easiest way to perform Rotation for Higher Order Tensors in Mathematica ? For Instance 4th order tensor
$C_{ijkl} = \lambda_{im}\lambda_{jn}\lambda_{ko}\lambda_{lp} C_{mnop}$
4
votes
0answers
49 views
5
votes
1answer
73 views
A simple problem on TensorTranspose
In the "Applications" part of TensorTranspose, it is given an example on the calculation of Christoffel according to metrics. I am confused about the definition of <...
-2
votes
1answer
278 views
How to reproduce this tensor calculation with Mathematica [closed]
The tensor operation shown in the red box is used in the textbook(P117-P120) to prove that there are only 9 independent constants for orthotropic materials:
I want to use MMA to reproduce the ...
-1
votes
1answer
192 views
How to use Mathematica to show why engineering strain is not a tensor [closed]
One of the most classical examples in the mechanics of materials is that engineering strain is not tensor. I want to use Mathematica to show why it doesn't meet the tensor requirements.
...
6
votes
3answers
547 views
How to implement Einstein summation convention with differential operators
Statement of this problem:
In the textbook, the following differential equilibrium equations can be expressed by tensors:
Using Einstein's summation convention, the formula in the figure above can be ...
2
votes
4answers
122 views
Calculate dot product of two tensor products in mathematica as tensorproduct
I would like to calculate
$$(\mathbb{1} \otimes \mathbb{1} \otimes \sigma^+)(\mathbb{1} \otimes \mathbb{1} \otimes \sigma^-) = (\mathbb{1} \otimes \mathbb{1} \otimes \left( \begin{array} \\ 1 &0 ...
0
votes
0answers
29 views
What should I do to get a fourth-order tensor with only two independent components
I see this example in help SymmetrizedIndependentComponents, We can see that matrix A has only four independent components:
<...
0
votes
0answers
69 views
How to prove that isotropic materials have only two independent constants by tensor operation rules [duplicate]
I want to use tensor method to prove that there are only two independent elastic constants for isotropic materials. But I can' t get two independent results after reading related posts.
The following ...
1
vote
0answers
53 views
Determinant of the tensor matrix in Mathematica? [closed]
I have a data:
As an example, it looks like this:
Then, when I try to take Det[]:
How we can find determinant value of these kind of matrices ?
3
votes
0answers
160 views
Spin Connection using Mathematica
Hello I want to use Mathematica in order to calculate the spin connection of a metric, specifically of the metric
\begin{equation}
\left(\begin{array}{cccc}
-1 & 0 & 0 & 0 \\
0 & \...
2
votes
2answers
95 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
51 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
53 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
55 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::...
3
votes
2answers
140 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
91 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
48 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
99 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
130 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
71 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
68 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
129 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
115 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
47 views
Parallelize and tensor calculus
Is it possible to use Parallelize with tensor calculus functions like TensorContract and ...
3
votes
1answer
64 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
62 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
429 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
122 views
TensorContract and TensorProduct problem
I am trying the calculate the Kretschmann scalar $K$ of a metric $$K=R^{abcd}R_{abcd}$$ where $R$ is the Riemann tensor. If I do
...
0
votes
1answer
50 views
How can I take the divergence of a symbolic vector? [duplicate]
I would like to compute expressions that have the following form:
$$\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^...
