LeviCivitaTensor

LeviCivitaTensor(n)

returns the n-dimensional Levi-Civita tensor as sparse array. The Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers 1, 2, …, n, for some positive integer n.

See:

• Wikipedia - Levi-Civita symbol

Examples

>> LeviCivitaTensor(4) // Normal
{{{{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}},{{0,0,0,0},{0,0,0,0},{0,0,0,1},{0,0,-
1,0}},{{0,0,0,0},{0,0,0,-1},{0,0,0,0},{0,1,0,0}},{{0,0,0,0},{0,0,1,0},{0,-1,0,0},{
0,0,0,0}}},{{{0,0,0,0},{0,0,0,0},{0,0,0,-1},{0,0,1,0}},{{0,0,0,0},{0,0,0,0},{0,0,
0,0},{0,0,0,0}},{{0,0,0,1},{0,0,0,0},{0,0,0,0},{-1,0,0,0}},{{0,0,-1,0},{0,0,0,0},{
1,0,0,0},{0,0,0,0}}},{{{0,0,0,0},{0,0,0,1},{0,0,0,0},{0,-1,0,0}},{{0,0,0,-1},{0,
0,0,0},{0,0,0,0},{1,0,0,0}},{{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}},{{0,1,0,0},{-
1,0,0,0},{0,0,0,0},{0,0,0,0}}},{{{0,0,0,0},{0,0,-1,0},{0,1,0,0},{0,0,0,0}},{{0,0,
1,0},{0,0,0,0},{-1,0,0,0},{0,0,0,0}},{{0,-1,0,0},{1,0,0,0},{0,0,0,0},{0,0,0,0}},{{
0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}}}}

Return the n-dimensional Levi-Civita tensor as a list by appending the symbol List

>> LeviCivitaTensor(3,List)
{{{0,0,0},{0,0,1},{0,-1,0}},{{0,0,-1},{0,0,0},{1,0,0}},{{0,1,0},{-1,0,0},{0,0,0}}}

Implementation status

• ☑ - partially implemented

Github

• Implementation of LeviCivitaTensor