SCORPION

The Levi-Civita symbol, also called the permutation symbol, antisymmetric symbol, or alternating symbol, is a mathematical symbol used in particular in tensor calculus. It is named after the Italian mathematician and physicist Tullio Levi-Civita.

In three dimensions, the Levi-Civita symbol is defined as follows

i.e. \varepsilon_{ijk} is 1 if (i, j, k) is an even permutation of (1,2,3), -1 if it is an odd permutation, and 0 if any index is repeated.

The formula in four dimensions is