PolynomialReduce[poly, , , ... , , , ... ] yields a list representing a reduction of poly in terms of the .
The list has the form , , ... , b, where b is minimal and + + ... + b is exactly poly.
The polynomial b has the property that none of its terms are divisible by leading terms of any of the .
If the form a Gröbner basis then this property uniquely determines the remainder obtained from PolynomialReduce.
The following options can be given, as for GroebnerBasis:
See The Mathematica Book: Section 3.3.4.
See also: GroebnerBasis, PolynomialRemainder, PolynomialMod.
Related package: Algebra`SymmetricPolynomials`.