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:
  • MonomialOrderLexicographicthe criterion used for ordering monomials
    CoefficientDomainRationalsthe types of objects assumed to be coefficients
    Modulus0the 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:

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

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Introduced in 1996
(3.0)