REDUCE package NCPOLY: Computation in non-commutative polynomial ideals. REDUCE supports a very general mechanism for computing with objects under a non–commutative multiplication, where commutator relations must be introduced explicitly by rule sets when needed. The package NCPOLY allows you to set up automatically a consistent environment for computing in an algebra where the non–commutativity is defined by Lie-bracket commutators. The package uses the REDUCE noncom mechanism for elementary polynomial arithmetic; the commutator rules are automatically computed from the Lie brackets. You can perform polynomial arithmetic directly, including division and actorization. Additionally NCPOLY supports computations in a one sided ideal (left or right), especially one sided Gröbner bases and polynomial reduction.