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based on an earlier version of the Wolfram Language.
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MonomialList

MonomialList[poly]
gives the list of all monomials in the polynomial poly.
MonomialList[poly, {x1, x2, ...}]
gives the list of monomials with respect to the variables xi in poly.
MonomialList[poly, {x1, x2, ...}, order]
puts the monomials in the specified order.
  • MonomialList works whether or not poly is explicitly given in expanded form.
  • Possible settings for order are "Lexicographic", "DegreeLexicographic", "DegreeReverseLexicographic", "NegativeLexicographic", "NegativeDegreeLexicographic", "NegativeDegreeReverseLexicographic" or an explicit weight matrix.
  • Monomials are sorted on the basis of their exponent vectors with respect to the variables xi.
  • "NegativeLexicographic" corresponds to applying Sort to the list of exponent vectors.
  • "Lexicographic" gives the reverse of "NegativeLexicographic", and is the default for MonomialList.
  • "DegreeLexicographic" sorts first with respect to total degree, then by using the ordering defined by "Lexicographic".
  • "DegreeReverseLexicographic" sorts first with respect to total degree, then in the negative lexicographic order by starting from the last variable.
  • "NegativeDegreeLexicographic" and "NegativeDegreeReverseLexicographic" sort from lower to higher total degree.
  • An explicit weight matrix w defines an ordering given by "Lexicographic" ordering of the w.vi, where the vi are the exponent vectors.
Get the list of monomials:
Get the list of monomials:
In[1]:=
Click for copyable input
Out[1]=
Use "DegreeLexicographic" monomial ordering:
Specify the same ordering using weight matrix:
Reduce the coefficients modulo 2:
Plus or Total reconstructs the original polynomial:
CoefficientRules gives a different representation:
Obtain "NegativeDegreeReverseLexicographic" from "DegreeLexicographic":
The list given by Variables[poly] is not always sorted:
New in 7