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NonCommutativeMonomialList[poly,vars,alg]

gives the list of all monomials in the polynomial poly in the variables vars over the non-commutative algebra alg.

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NonCommutativeMonomialList

NonCommutativeMonomialList[poly,vars,alg]

gives the list of all monomials in the polynomial poly in the variables vars over the non-commutative algebra alg.

Details

  • List of monomials in a polynomial over a non-commutative algebra.
  • The monomials are listed in the decreasing order. The monomial order is determined by vars.
  • vars should be {vs1,…,vsk}, where vsi are disjoint lists of variables that include all non-commutative variables that appear in poly. vsi=x, where x is a variable, is equivalent to vsi={x}.
  • vars determines a multi-graded lexicographic monomial order. The monomials are ordered first on the number of occurrences of variables from vsi, with the smallest i for which the numbers differ, then on the number of occurrences of the commutative variables from alg. If all numbers of occurrences are the same, monomials are ordered lexicographically on Flatten[vars] and then lexicographically on the commutative variables from alg.
  • alg can be a NonCommutativeAlgebra object, {Dot,n}, Composition, TensorProduct or NonCommutativeMultiply. If the algebra argument is omitted, NonCommutativeAlgebra with the default property values is used.

Examples

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Basic Examples  (2)

Get the list of monomials in decreasing order with :

List of monomials in a polynomial over an algebra with symbolic operations:

Scope  (1)

For two variables, four different monomial orders can be specified:

Properties & Relations  (1)

Applying the algebra addition to the monomial list gives the expanded form of the polynomial:

Wolfram Research (2025), NonCommutativeMonomialList, Wolfram Language function, https://reference.wolfram.com/language/ref/NonCommutativeMonomialList.html.

Text

Wolfram Research (2025), NonCommutativeMonomialList, Wolfram Language function, https://reference.wolfram.com/language/ref/NonCommutativeMonomialList.html.

CMS

Wolfram Language. 2025. "NonCommutativeMonomialList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonCommutativeMonomialList.html.

APA

Wolfram Language. (2025). NonCommutativeMonomialList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonCommutativeMonomialList.html

BibTeX

@misc{reference.wolfram_2025_noncommutativemonomiallist, author="Wolfram Research", title="{NonCommutativeMonomialList}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/NonCommutativeMonomialList.html}", note=[Accessed: 04-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_noncommutativemonomiallist, organization={Wolfram Research}, title={NonCommutativeMonomialList}, year={2025}, url={https://reference.wolfram.com/language/ref/NonCommutativeMonomialList.html}, note=[Accessed: 04-August-2025]}