Computes the Generalized Kronecker Delta.

delta(n, p = 1)

Arguments

n

number of elements for each dimension.

p

order of the generalized Kronecker delta, p=1 for the standard Kronecker delta.

Value

array representing the generalized Kronecker delta tensor.

References

Guidotti, E. (2020). "calculus: High dimensional numerical and symbolic calculus in R". https://arxiv.org/abs/2101.00086

See also

Other tensor algebra: contraction(), diagonal(), einstein(), epsilon(), index()

Examples

### Kronecker delta 3x3 delta(3)
#> [,1] [,2] [,3] #> [1,] 1 0 0 #> [2,] 0 1 0 #> [3,] 0 0 1
### generalized Kronecker delta 3x3 of order 2 delta(3, p = 2)
#> , , 1, 1 #> #> [,1] [,2] [,3] #> [1,] 0 0 0 #> [2,] 0 0 0 #> [3,] 0 0 0 #> #> , , 2, 1 #> #> [,1] [,2] [,3] #> [1,] 0 -1 0 #> [2,] 1 0 0 #> [3,] 0 0 0 #> #> , , 3, 1 #> #> [,1] [,2] [,3] #> [1,] 0 0 -1 #> [2,] 0 0 0 #> [3,] 1 0 0 #> #> , , 1, 2 #> #> [,1] [,2] [,3] #> [1,] 0 1 0 #> [2,] -1 0 0 #> [3,] 0 0 0 #> #> , , 2, 2 #> #> [,1] [,2] [,3] #> [1,] 0 0 0 #> [2,] 0 0 0 #> [3,] 0 0 0 #> #> , , 3, 2 #> #> [,1] [,2] [,3] #> [1,] 0 0 0 #> [2,] 0 0 -1 #> [3,] 0 1 0 #> #> , , 1, 3 #> #> [,1] [,2] [,3] #> [1,] 0 0 1 #> [2,] 0 0 0 #> [3,] -1 0 0 #> #> , , 2, 3 #> #> [,1] [,2] [,3] #> [1,] 0 0 0 #> [2,] 0 0 1 #> [3,] 0 -1 0 #> #> , , 3, 3 #> #> [,1] [,2] [,3] #> [1,] 0 0 0 #> [2,] 0 0 0 #> [3,] 0 0 0 #>