How to | Rearrange the Terms of a Polynomial

The Wolfram Language provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary expression structures.

Define a polynomial in and exponentials of :

Collect the powers of :

Group terms that match the pattern; in this case terms that have the same exponential factors are grouped:

Apply Simplify to the coefficient of each term after collecting the terms:

    

There are many ways to extract terms from an expression. Here is a polynomial in :

Get the coefficient of (the constant term):

Get the same term by replacing with zero, thus eliminating all terms that depend on :

Get the list of the monomials ordered from high to low powers of :

The polynomial will appear in the same order when displayed in TraditionalForm:

  • Algebraic Manipulation
  • Polynomial Orderings
  • How to: Do Algebraic Calculations
  • Collect  Simplify  Coefficient  MonomialList  Factor  Exponent  CoefficientRules

  • Polynomial Algebra
  • "How to" Topics