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

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Reduce a polynomial with respect to a list of polynomials :

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

is a linear combination of polynomials and a remainder term :

In[3]:=
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Out[3]=
Introduced in 1996
(3.0)
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