GrassmannAlgebra

GrassmannAlgebra[vars]
GrassmannAlgebra[vars, alg]

constructs a NonCommutativeAlgebra representing the Grassmann, or exterior, algebra with generators vars.

Example

alg = GrassmannAlgebra[{x, y, z}];
NonCommutativeExpand[
  Wedge[x + 2 y + 3 z, 4 x + 5 y + 6 z],
  alg
]

The generators anticommute and their squares vanish.

See the official Wolfram Language reference for the canonical representation and supported operations.