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.
32
votes
2answers
980 views
Internal`Bag inside Compile
Since Internal`Bag, Internal`StuffBag and Internal`BagPart can be compiled down, it is a ...
6
votes
4answers
2k views
How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica?
I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. ...
13
votes
2answers
749 views
How to represent and manipulate abstract indexed vector (or tensor) expressions?
I have a couple abstract indexed quantities, both differential elements
$dx = dx^\mu e_\mu + x^\mu de_\mu$
$du = du^\mu e_\mu + u^\mu de_\mu$
I can compute the expression $(dx + du) \cdot (dx + du) ...
10
votes
1answer
348 views
Nesting Parallel processes
I just attempted to run code that had nested ParallelMap[] functions. It generates the error message:
ParallelMap::subpar: Parallel computations cannot be nested;
proceeding with sequential ...
5
votes
3answers
334 views
Ways to compute inner products of tensors
One way to evaluate the following sums is combining Table and Sum:
$u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$
$q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$
It will look like
...
7
votes
1answer
162 views
Compiling Map over expression that yields a ragged array
I'm trying to speed up a function that looks in the neighborhood of each 3D point in a large dataset and finds all the points within 1 unit in each direction, x, y, z.
I've started by using ...
5
votes
1answer
293 views
Tensor analysis
Has anybody used tensors in Mathematica? How to properly work with them?
I find Mathematica not very friendly in this field, as I am defining my own functions for lowering & raising indices, ...
5
votes
1answer
201 views
Solving antisymmetric tensorial equation
Assume we have the following Tensor objects:
\begin{equation}
F_{i}{}^{j}\;and\;S_{ij}{}^{k},
\end{equation}
where the components of $F$ are known, and we would like to solve for the components of $S$ ...
-2
votes
0answers
88 views
How to type function terms into metric?
I submitted my question before on site:Anything wrong with Atlas 2 or Mathematica?. Due to my vagueness, my problems might not be clearly understood.
I am trying to solve several functions based on ...
