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.

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9
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0answers
152 views

Can I use symbolic tensors for simple linear algebra and calculus?

As an example, I'd like to calculate this symbolic derivative: $\frac{\partial}{\partial b}(x-A.b)^{\mathsf{T}}.(x-A.b)$ where $x$ and $b$ are vectors and $A$ is a matrix. What I tried is this: ...
8
votes
0answers
162 views

Efficient way to flatten or transpose-arrayreshape tensors

I have a tensor of dimensions $(2, 100, 100, 2, 100, 100)$ and I want to reshape it to a form of $(2*100*100,2*100*100)$, e.g. Flatten[A,{{1,5,6},{4,2,3}}]. If I ...
4
votes
0answers
71 views

How to write Coordinate Chart in Xcoba in index form?

I am using xCoba for manipulating tensors. I do the usual, defining my metric, manifold, chart etc. ...
3
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0answers
57 views

Nested TensorContract bug

Bug introduced in version 9.0.0 or 9.0.1 and fixed in 10.1 or 10.2 When nesting TensorContract the result I get is wrong. Input: ...
3
votes
0answers
574 views

how to associate a metric for tensor contraction operations?

I see that Version 9 now has some built in tensor support (which was missing back when previously asked How to represent and manipulate abstract indexed vector (or tensor) expressions?). The docs ...
2
votes
0answers
21 views

How to deal with tensor argument in LibraryLink?

For the B├ęzier surface, which owns the following matrix definition: $$\begin{align*} \mathbf{S}(u,v)&=\sum_{i=0}^m \sum_{j=0}^n \mathbf{P}_{i,j} B_{i,m}(u) B_{j,n}(v)\\ &=\small \begin{...
2
votes
0answers
58 views

Simplifying symbolic expressions using TensorExpand

Following my previous question I have this issue using TensorExpand: KroneckerProduct[x, y].(KroneckerProduct[2 z, w]) // TensorExpand results in ...
2
votes
0answers
56 views

Arrays with two different types of indices

Is there a way of having arrays which have, so to speak, two different depths $m,n$? From the point of view of memory usage, it would be the same as an array of depth $m+n$, but I would like to ...
2
votes
0answers
95 views

Fast construction and reshaping of large tensors

I'm trying to construct a large matrix which is derived from some higher rank tensor (the rank of interest to me changes case by case, so it needs to be a general method). Currently, the process of ...
2
votes
0answers
57 views

Finding basis of isotropic tensors of rank r

I am looking for a way to obtain a basis of isotropic tensors of rank $r$. Actually I am mostly interested in rank $8$ isotropic tensors but maybe you know already a simple algorithm in order to ...
2
votes
0answers
200 views

SymmetrizedArray of stiffness/compliance tensor

The stiffness and compliance tensors of a material are 3x3x3x3 tensors relating stress and strain. ...
2
votes
0answers
135 views

How to solve system of differential equations of arbitrary order (symbolic tensors)?

I am interested in solving systems of ODEs symbolicly, keeping things with arbitrary dimensions for clarity. For example, assume that $x, f(x) \in R^N$ and $A \in R^{N \times N}$, how do I solve $f'(...
2
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0answers
121 views

Prevent Suppression of Superscript 1 in Print

I'm trying to print Christoffel symbols of the second kind for a surface in $\mathbb R^3$. I currently am using something along the lines of ...
2
votes
0answers
132 views

Smooth Max and Abs

I'm trying to implement smooth approximations of Max and Abs functions. Moreover I want the functions to map element-wise on tensors. Here's my code. ...
1
vote
0answers
98 views

Outer product using the quantum mathematica package

I am using the quantum Mathematica package and am trying to do computations that require me to use the outer (tensor) products of Pauli matrices. I would define this as, for example, ...
1
vote
0answers
60 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
1
vote
0answers
27 views

Assign a symbolic tensor with determinant greater than zero in Mathematica

I can create a symbolic tensor in Mathematica: $Assumptions = F \[Element] Arrays[{3, 3}, Reals] Is there anyway that I can tell Mathematica, that the ...
1
vote
0answers
158 views

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
1
vote
0answers
86 views

How does TensorReduce use assumptions?

I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce: ...
0
votes
0answers
59 views

Scalar from tensor contraction

I'm trying to calculate the Kretschmann scalar in mathematica, it is given by: $c = R^{abcd} R_{abcd}$ Where $R^{abcd}$ is the Riemann tensor. I'm following this MSE post so I modified it to ...
0
votes
0answers
217 views

Symbolic Tensor Algebra

I need to perform basic tensor algebra in order to double check some very complicated simplification. It's nothing fancy, it just has so many factors by the end that it's hard to tell if an error has ...
0
votes
0answers
321 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\...