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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36 views

Change of basis for a rank 3 Cartesian tensor

I have a Cartesian tensor $\chi_{ijk}$ and I want to express the elements in terms of a new basis to get $\chi_{ijk}^\prime$. The transformation is represented using $a_{ij}$. The tensor transforms ...
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1answer
22 views

How to take derivative of a tensor leading to kronecker delta?

I'm trying to write a Mathematica program to find derivatives such as the following simple example: Could you please help?
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0answers
451 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
5
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0answers
88 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: ...
2
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0answers
91 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 ...
2
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0answers
107 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
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0answers
121 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. ...
2
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0answers
407 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 ...
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0answers
72 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: ...
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0answers
36 views

Get rid of external library dependency

I am trying to generate C code for some functions, which I do not post in full because they are a few hundred lines long. The functions do nothing too fancy: a bunch of dot products, powers and roots. ...
0
votes
0answers
117 views

Symbolic tensor product calculation

I am trying to calculate the 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 ...
0
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0answers
60 views

g00 (metric tensor) not explicitly evaluated in FeynCalc

I am learning Mathematica and FeynCalc by doing some basic cross section calculations. I have an issue with trace calculations: When I plug in for instance the ...