] yields a list representing a reduction of poly in terms of the .
The list has the form
, 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`.
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.
This reduces assuming that the polynomials in the list are zero.
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.
See the Further Examples for GroebnerBasis.