# 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 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

# Examples

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## Basic Examples(1)

Reduce a polynomial f with respect to a list of polynomials p:

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

 In:= Out= ## Properties & Relations(3)

Introduced in 1996
(3.0)