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:

Scope  (1)

Use "DegreeLexicographic" monomial ordering:

Specify the same ordering using a weight matrix:

Options  (1)

Modulus  (1)

Reduce the coefficients modulo 2:

Properties & Relations  (2)

Plus or Total reconstructs the original polynomial:

CoefficientRules gives a different representation:

Obtain "NegativeDegreeReverseLexicographic" from "DegreeLexicographic":

Possible Issues  (1)

The list given by Variables[poly] is not always sorted:

Wolfram Research (2008), MonomialList, Wolfram Language function, https://reference.wolfram.com/language/ref/MonomialList.html.

Text

Wolfram Research (2008), MonomialList, Wolfram Language function, https://reference.wolfram.com/language/ref/MonomialList.html.

CMS

Wolfram Language. 2008. "MonomialList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MonomialList.html.

APA

Wolfram Language. (2008). MonomialList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MonomialList.html

BibTeX

@misc{reference.wolfram_2024_monomiallist, author="Wolfram Research", title="{MonomialList}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/MonomialList.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_monomiallist, organization={Wolfram Research}, title={MonomialList}, year={2008}, url={https://reference.wolfram.com/language/ref/MonomialList.html}, note=[Accessed: 22-December-2024 ]}