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.

Details and Options

  • MonomialList works whether or not poly is explicitly given in expanded form.
  • MonomialList[poly] is equivalent to MonomialList[poly,Variables[poly]].
  • 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.
  • MonomialList[poly,vars,Modulus->m] computes the coefficients modulo m.
  • MonomialList[poly,All,order] is equivalent to MonomialList[poly,Variables[poly],order].

Examples

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Basic Examples  (1)

Get the list of monomials:

In[1]:=
Click for copyable input
Out[1]=

Scope  (1)

Options  (1)

Properties & Relations  (2)

Possible Issues  (1)

See Also

Collect  Variables  Exponent  CoefficientList  CoefficientRules  GroebnerBasis

Tutorials

Introduced in 2008
(7.0)