NonCommutativeGroebnerBasis

NonCommutativeGroebnerBasis[{poly1, poly2, ...}, vars, alg]
NonCommutativeGroebnerBasis[{poly1, poly2, ...}, alg]

attempts to compute a reduced Gröbner basis for non-commutative polynomials. When alg declares its generators, the explicit vars argument can be omitted.

Example

NonCommutativeGroebnerBasis[
  {x ** y - y ** x, x ** x - x},
  {x, y}
]

The result depends on the algebra and the monomial ordering.

See the official Wolfram Language reference for ordering options and left ideals.