NonCommutativePolynomialReduce

NonCommutativePolynomialReduce[poly, {poly1, poly2, ...}, vars, alg]
NonCommutativePolynomialReduce[poly, {poly1, poly2, ...}, alg]

reduces poly modulo a list of non-commutative polynomials. It returns reduction functions together with the remainder.

Example

p = x ** x ** y + y ** x;
divisors = {x ** y - y ** x};

{functions, remainder} =
  NonCommutativePolynomialReduce[p, divisors, {x, y}]

Use NonCommutativeExpand when verifying the reconstructed polynomial.

See the official Wolfram Language reference for the result structure and ordering rules.