Computes the Levi-Civita totally antisymmetric tensor.
epsilon(n)
number of dimensions.
array
representing the Levi-Civita symbol.
Guidotti, E. (2020). "calculus: High dimensional numerical and symbolic calculus in R". https://arxiv.org/abs/2101.00086
Other tensor algebra:
contraction()
,
delta()
,
diagonal()
,
einstein()
,
index()
### Levi-Civita symbol in 2 dimensions
epsilon(2)
#> [,1] [,2]
#> [1,] 0 1
#> [2,] -1 0
### Levi-Civita symbol in 3 dimensions
epsilon(3)
#> , , 1
#>
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 0 0 1
#> [3,] 0 -1 0
#>
#> , , 2
#>
#> [,1] [,2] [,3]
#> [1,] 0 0 -1
#> [2,] 0 0 0
#> [3,] 1 0 0
#>
#> , , 3
#>
#> [,1] [,2] [,3]
#> [1,] 0 1 0
#> [2,] -1 0 0
#> [3,] 0 0 0
#>