CliffordAlgebra

CliffordAlgebra[{pvars, nvars, zvars}]
CliffordAlgebra[{pvars, nvars, zvars}, alg]

constructs a NonCommutativeAlgebra representing a generalized Clifford algebra. Generators in pvars, nvars and zvars square to 1, -1 and 0, respectively.

Example

alg = CliffordAlgebra[{{e1, e2}, {e3}, {}}];
NonCommutativeExpand[(e1 + e3) ** (e1 - e3), alg]

The second form takes operation names and monomial-order settings from alg.

See the official Wolfram Language reference for the defining relations.