This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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. In[1]:= Out[1]= In[2]:= Out[2]= In[3]:= Out[3]= In[4]:= Out[4]= In[5]:= This reduces assuming that the polynomials in the list are zero. In[6]:= Out[6]= 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. In[7]:= Out[7]= In[8]:= Out[8]= In[9]:= See the Further Examples for GroebnerBasis.