CoefficientRules

CoefficientRules[poly,{x1,x2,}]

gives the list {{e11,e12,}c1,{e21,}c2,} of exponent vectors and coefficients for the monomials in poly with respect to the xi.

CoefficientRules[poly,{x1,x2,},order]

gives the result with the monomial ordering specified by order.

Examples

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Basic Examples(1)

Get exponents and coefficients of monomials:

Scope(1)

Use "DegreeReverseLexicographic" monomial ordering:

Specify the same ordering using weight matrix:

Options(1)

Modulus(1)

Reduce the coefficients modulo 2:

Properties & Relations(2)

FromCoefficientRules reconstructs the original polynomial:

MonomialList gives a different representation:

For two variables "DegreeLexicographic" and "DegreeReverseLexicographic" coincide:

Possible Issues(1)

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

Neat Examples(2)

Visualize monomial orderings in 2D:

The standard built-in orderings:

In 2D some orderings cannot be distinguished:

Visualize monomial orderings in 3D:

In 3D all orderings are distinct:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_coefficientrules, author="Wolfram Research", title="{CoefficientRules}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/CoefficientRules.html}", note=[Accessed: 31-May-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_coefficientrules, organization={Wolfram Research}, title={CoefficientRules}, year={2008}, url={https://reference.wolfram.com/language/ref/CoefficientRules.html}, note=[Accessed: 31-May-2023 ]}