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 in poly.

MonomialList[poly, {x1, x2, ...}, order]
puts the monomials in the specified order.

Details and OptionsDetails 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 , , , , , , or an explicit weight matrix.
  • Monomials are sorted on the basis of their exponent vectors with respect to the variables .
  • corresponds to applying Sort to the list of exponent vectors.
  • gives the reverse of , and is the default for MonomialList.
  • sorts first with respect to total degree, then by using the ordering defined by .
  • sorts first with respect to total degree, then in the negative lexicographic order by starting from the last variable.
  • and sort from lower to higher total degree.
  • An explicit weight matrix w defines an ordering given by ordering of the , where the 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].
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