BUILT-IN MATHEMATICA 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]=

## TutorialsTutorials

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