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CoefficientRules

CoefficientRules
gives the list of exponent vectors and coefficients for the monomials in poly with respect to the .
CoefficientRules
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:
In[1]:=
Click for copyable input
Out[1]=
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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