Built-in Mathematica Symbol

PolynomialReduce

PolynomialReduce[poly, {poly₁, poly₂, ...}, {x₁, x₂, ...}]
yields a list representing a reduction of poly in terms of the poly_i. The list has the form {{a₁, a₂, ...}, b}, where b is minimal and a₁ poly₁+a₂ poly₂+... +b is exactly poly.

MORE INFORMATION

The polynomial b has the property that none of its terms are divisible by leading terms of any of the poly_i.

If the poly_i form a Gröbner basis then this property uniquely determines the remainder obtained from PolynomialReduce.

The following options can be given, as for GroebnerBasis:

MonomialOrder	Lexicographic	the criterion used for ordering monomials
CoefficientDomain	Rationals	the type of objects assumed to be coefficients
Modulus	0	the modulus for numerical coefficients