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.
481
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What is the right way to simplify a tensor expression (with many indices, but no derivatives) in Mathematica?
After not finding the desired capabilities in base Mathematica, I am trying to use xAct`xTensor package. It appears that I do not need most of it capabilities ...
- 166
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0
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Simplification of Momentums in FeynCalc
I have a little problem involving the following contraction in FeynCalc:
$$\frac{k^{\delta}k^{\sigma}}{k^2}$$
By hand one would lower $\sigma$ and contract with the other momentum to cancel $k^2$, ...
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4
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How can I "multiply" nested lists?
Given two nested lists
alist={{a,b,c},{d,e,f}}
blist={{r,s,t},{x,y,z}}
How can I get
...
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0
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How to multiply five tensors of different ranks (contravariant, covariant and mixed) in Mathematica?
How to compute the following multiplication of five different tensors of different ranks in Mathematica
...
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2
answers
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Symbolic matrix tensor an identity without specifying the dimension?
I want to calculate an expression like $\left( M_1\otimes I+I\otimes M_2 \right) ^l$ with $M_i$'s symbolic matrices and $I$ the identity matrix with Mathematica. $M_i$'s are of the same dimension and ...
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TensoriaCalc does not display the correct output
I am trying to use TensoriaCalc to calculate the components of the Ricci and the Riemann tensor of the following metric: $R^{2} \left(d\theta^{2} + \sin^{2}\left(\theta \right)d\phi^{2} \right)$;
...
- 111
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Mathematica, ML and TensorFlow
I am currently studying a specialization on Coursera in Machine Learning and am investigating various tools to help me out with the maths and with visualisations and so on.
Although I have many ...
- 111
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4
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1
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Quickly summing matrix elements
I have a pair of rank-4 tensors, (T,V), where each index takes four values. I want to quickly contract these with the rank-4 antisymmetric tensor using the following operation:
...
- 647
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49
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Polar to Cartesian coordinate transformations [duplicate]
I'm trying to plot the energy boundary function EBminus[r, \theta, LL, S, BB] using Polar to Cartesian coordinate transformations. The plot should be a closed curve....
- 87
2
votes
1
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Pathological expression for field strength contractions in a curved background
I am trying to define in Mathematica the quantity $\star F^{\mu}=\frac{1}{2}\epsilon^{\mu\alpha\beta}F_{\alpha\beta}$, where $F_{\mu\nu}=\nabla_\mu A_\nu-\nabla_\nu A_\mu+\left[A_\mu,A_\nu\right]$. ...
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Simulation of Quantum pseudo-telepathy
I would like to mathematically simulate Quantum pseudo-telepathy on The magic square game from Wikipedia.
In section Pseudo-telepathic strategies we can read:
The trick is for Alice and Bob to share ...
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Why is TensorContract[x, {}] not always x?
If I use TensorTranspose on an undefined symbol, nothing happens unless the permutation is the identity. For instance, ...
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0
answers
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Tensor equation problem (xact package)
So i want to solve the tensor equation P1[-μ,-ν]=0 with respect to A[r] and then B[r] but the problem is when hitting shift-enter the tensor given is way too long (if i press "show all" my ...
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7
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Fast Sparse Tensor Addition
How can one do a fast sparse tensor addition?
Below, I have the following code: We first generate 3 random sparse 1000x1000x1000 tensors with 10^6 entries each.
Then, I want to add them. But the usual ...
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1
answer
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How to define a traceless tensor with xAct
I would like to define a tensor $A_i^j$ which is traceless ($A_i^i = 0$) and to obtain $A_i^j \delta^i_j = 0$ with xAct / xTensor / xCoba.
I first tried defining an antisymmetric tensor, since they ...
- 386
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2
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Code for Tensor decomposition
I would like to know if there is a package or some MMA code to perform tensor decomposition as e.g. defined in a paper by Robeva "Orthogonal decomposition of symmetric tensors" or some ...
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2
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"Symmetrize" shall symmetrize only tensor values $\ne 0$
Using Symmetrize I want to transform a tensor to be symmetric under all index permutations for all original entries $\ne 0$. However each entry is normalized by the ...
- 690
0
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1
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93
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Is there a way of calculating Expectation Values of tensor operators in Mathematica?
This Wikipedia article in on Bell's Theorem lists a whole bunch of expectation values for Bell states:
$$\langle A_0 \otimes B_0 \rangle = \frac{1}{\sqrt{2}}, \langle A_0 \otimes B_1 \rangle = \frac{1}...
- 243
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2
answers
325
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Torch-like permutation for arrays?
Update: edited to clarify my confusion.
In Mathematica Transpose[] operates like this:
...
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votes
2
answers
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Symmetric product
Let define the full symmetrization of a tensor $e_1 \otimes ... \otimes e_N$ by
$$ Sym : e_1 \otimes ... \otimes e_N \rightarrow \frac{1}{N!} \sum_{\pi \in S_N} e_{\pi^{-1} (1)} \otimes ... \otimes e_{...
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1
answer
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Certain block matrix
A block matrix like
$$m_{(ij),(kl)}=\delta_{ik}\delta_{jl}$$
can be constructed as
L=3;
id=IdentityMatrix[L];
m=KroneckerProduct[id, id];
But how to construct
$$m_{...
- 17k
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0
answers
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Error message installing Ricci
I just started using Mathematica. With the goal of solving
a Loop integrals over a scalar gravity interaction. For the tensor calculus necessary i wanted to use, Ricci. https://sites.math.washington....
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How to generate a tensor by a given list, which specifies the ranges and dimensions of the tensor?
I am trying to create a function that generates a tensor according to a list, each of whose elements specifies the range of the corresponding dimension of the tensor and whose length specifies the ...
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2
votes
1
answer
114
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Reshape a tensor to a matrix
I have a tensor
T = Array[Subscript[K, ##] &, {2, 2, 2, 2}]
And its matrix form is
$$
\left(
\begin{array}{cc}
\left(
\begin{array}{cc}
...
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4
votes
1
answer
67
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xAct define normalization
I'm trying to get out some equations in the xAct suite. I would like to somehow define that the norm of a vector is a constant.
...
- 438
4
votes
3
answers
159
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Using Flatten inside NDSolve
I'm using Flatten to contract a rank 4 tensor and a matrix (rank 2 tensor) inside NDSolve and there seems to be error. Here is ...
- 65
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0
answers
29
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Using Manipulate to both change tensor elements and select different tensors
I want to display three different tensors after I transform them within the manipulate function
I have three tensors that I want to transform, C1, C1h, and C2, then change through with a PopUpMenu to ...
- 27
1
vote
1
answer
84
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How to produce plots determined by tensor element manipulate function
I want to produce plots within the manipulate function, with the functions determined by the values that I use in the manipulate function.
I've gotten the tensor elements to work fine in producing the ...
- 27
0
votes
1
answer
56
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Symbolic re-assignment of products
Suppose I have some symbolic tensors $X,Y$ and I want to assign
X.Y
into something else without specifying what $Y$ is. For example, I may want $Y$ to serve as ...
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0
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How to get simplified output of tensor mode product [duplicate]
The code
PolarizationiC1 = MatrixForm[chiprimeC1 . Epin] . Esin;
The result
If I run the result, then I get the simplified answer of
...
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1
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1
answer
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How to make an inverse operation to `KroneckerProduct[A, IdentityMatrix[m]]` (simplify matrix)?
The operation KroneckerProduct[A, IdentityMatrix[m]] expands the matrix A in the following way (depending on order of ...
- 3,399
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1
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90
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How to untensor a tensor?
What should I do to convert a matrix of matrices to a non-nested matrix?
$\left(
\begin{array}{cc}
\left(
\begin{array}{cc}
{a_1} & {b_1} \\
{c_1} & {d_1} \\
\end{array}
\right) & \left(...
- 3,399
1
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3
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107
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How can I realize this matrix product (dot product of matrices of different orders)?
The matrix multiplication of square matrices of different order is often claimed to be impossible. Yet, if the order of one matrix is divisible by the order of the other, a natural multiplication rule ...
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3
votes
1
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161
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How to define a Tensor with the symmetries like Riemann tensor?
I want to define a tensor that has the first two symmetries of Riemann tensor or maybe the last two. The symmetries of Riemann tensor are:
1) $ R_{\alpha\beta\gamma\lambda}=R_{\gamma\lambda\alpha\beta}...
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9
votes
3
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164
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Doing ArrayReshape in Mathematica doesn't give desired results
I have an array like this for example,
a = ArrayReshape[Range[16], {4, 4}]
\begin{align}
\left(
\begin{array}{cccc}
1 & 2 & 3 & 4 \\
5 & 6 & ...
- 549
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0
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43
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Output of expressions unable to have operations be performed on the expression
I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as
n := 4
...
- 119
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1
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189
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Covariant Derivative
I'm trying to create a function which receives as inputs a coordinate system $x^\mu$, metric tensor $g_{\mu\nu}$, a general tensor $T$ of rank $n$, and a list $I$ of length $n$ that looks like this:
$$...
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0
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104
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Variation with respect to inverse metric in a Lagrangian density
I am trying to vary the following Lagrangian density
with respect to the inverse metric appearing in the equation, but I am having trouble with how to write the right code in Mathematica.
I have ...
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2
answers
134
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Set of quadratic forms and linear algebra
I have a set of quadratic forms.
$L_{1}=u_1^TJ_{1}u_1$
$L_{2}=u_2^TJ_{2}u_2$
$L_{3}=u_3^TJ_{3}u_3$
where $u_{i=1,2,3}$ - 3$\times$1 vector;
where $J_{i=1,2,3}$ - 3$\times$3 matrix;
I need to pack ...
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Tensorial calculus: A question about free and summed indices
I have to start with a full disclosure that I'm new to Mathematica, so this might be easy to resolve in a way that I don't know.
I have to implement a triple contraction of an order three tensor
$$d^{...
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159
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Create a tensor with a well defined symmetry
I want to create a symmetric rank four tensor with this kind of symmetry: {1,2} and {3,4}.
How can I implement this using "Array"?
...
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How to compute the divergence of a four-vector?
I have a quadri-vector which is given by
u = {(E^(-φ0[r]))*(1 - ε δφ[t,
r]), (E^(-φ0[r])) D[ε ξ[t, r], t], 0,
0}
and a quantity n which is given by
<...
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1
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183
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Mathematica: Partial derivative with respect to tensors
Anyone know how to do the partial derivative of a tensor in d dimensions on Mathematica ?
I want to implement something which will calculate directly like that :
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4
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86
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How to sum over a two tensor with a simple constraint of the form $i<j$?
I am trying to write a sum of the form
$$\sum_{i<j}f_{ij}$$
where $i,j\in \{1,2,3,4\}.$
I want to write something like Sum[f[[i,j]], {j,1,4},{i,1,j}]
but then ...
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0
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176
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Manipulating tensorial terms with xAct, ToCanonical is not perfoming well
I am trying to calculate perturbations of some complicated Lagrangians. Using xAct and more specifically VarD to perform the perturbations the expressions become ...
- 41
3
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1
answer
192
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Creating a rank 4 tensor
I am struggling with creating the rank-4 matrix T in Mathematica. The matric is defined as
$T_{i,j,k,l}= n_i n_j n_k n_l-(\delta_{i,j} n_k n_l +\delta_{i,k} n_j n_l+\delta_{i,l} n_k n_j+\delta_{j,l} ...
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How do I get the Schwarzschild solution from the Einstein Equations?
Consider the Schwartzchild-like metric $$ds^2=-A(r)dt^2+B(r)dr^2+r^2(d\theta^2+\sin^2\theta d\phi^2).$$ The Einstein field equations for this metric reduce to $$R_{\mu\nu}=0,$$ which is also known as ...
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497
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How to do Einstein Summation in Mathematica?
I am working with the de Sitter metric which takes the form
$$g=\tau^{-2}\left(-\left(\Lambda / 3-\tau^{2}\right)^{-1} d \tau^{2}+\left(\Lambda / 3-\tau^{2}\right) d t^{2}+g_{\mathbb{S}^{2}}\right)$$
...
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Simple and efficient construction of tensor product operators
Problem Description
I'm using mathematica to study a problem in quantum mechanics, which is naturally understood in terms of vector spaces. In the simplest example, suppose we have a 16-dimensional ...
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