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PolynomialReduce

  • PolynomialReduce[ poly , , , ... , , , ... ] yields a list representing a reduction of poly in terms of the .
  • The list has the form , , ... , b , where b is minimal and + + ... + b is exactly poly.
  • 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:
  • See the Mathematica book: Section 3.3.4.
  • See also: GroebnerBasis, PolynomialRemainder, PolynomialMod.
  • Related package: Algebra`SymmetricPolynomials`.

    Further Examples

    In the polynomial every term is divisible by either a or x, so reducing by a and x, in either order, gives . We check that we recover the original polynomial.

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    This reduces assuming that the polynomials in the list are zero.

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    We form a Groebner basis from a list of polynomials. When we reduce one of the polynomials (here the last one) in that Groebner basis by a different Groebner basis for the same list, we get zero.

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    See the Further Examples for GroebnerBasis.