This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


gives the list of exponent vectors and coefficients for the monomials in poly with respect to the .
gives the result with the monomial ordering specified by order.
  • CoefficientRules works whether or not poly is explicitly given in expanded form.
  • Possible settings for order are the same as in MonomialList.
  • The default order is .
Get exponents and coefficients of monomials:
Get exponents and coefficients of monomials:
Click for copyable input
Use monomial ordering:
Specify the same ordering using weight matrix:
Reduce the coefficients modulo 2:
FromCoefficientRules reconstructs the original polynomial:
MonomialList gives a different representation:
For two variables and coincide:
The list given by Variables[poly] is not always sorted:
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:
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