Commutator

Description

Commutator[x, y] = c defines the commutator between the non-commuting objects x and y.

See also:  AntiCommutator, CommutatorExplicit, DeclareNonCommutative, DotSimplify.

Examples

DeclareNonCommutative[a, b, c, d]

Commutator[a, b]

CommutatorExplicit[%]

DotSimplify[Commutator[a + b, c + d]]

UnDeclareNonCommutative[a, b, c, d]

Verify the Jacobi identity.

χ = Commutator;  DeclareNonCommutative[x, y, z];

χ[x, χ[y, z]] + χ[y, χ[z, x]] + χ[
        z, χ[x, y]]

DotSimplify[%]

Clear[χ]

UnDeclareNonCommutative[x, y, z]