# Wolfram Language & System 11.0 (2016)|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 polyi. The list has the form {{a1,a2,},b}, where b is minimal and a1 poly1+a2 poly2++b 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 polyi.
• If the polyi 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 types 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 f with respect to a list of polynomials p:

 In[1]:=
 In[2]:=
 Out[2]=

f is a linear combination of polynomials p and a remainder term r:

 In[3]:=
 Out[3]=