# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# PolynomialReduce

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

## Details and OptionsDetails and Options

• 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:
•  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

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

Reduce a polynomial with respect to a list of polynomials :

 Out[2]=

is a linear combination of polynomials and a remainder term :

 Out[3]=