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How to | Rearrange the Terms of a Polynomial
Mathematica 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 
:
| In[2]:= |
| Out[2]= |  |
Collect the powers of 
:
| In[3]:= |
| Out[3]= |  |
Group terms that match the pattern; in this case terms that have the same exponential factors are grouped:
| In[4]:= |
| Out[4]= |  |
Apply Simplify to the coefficient of each term after collecting the terms:
| In[5]:= |
| Out[5]= |  |
There are many ways to extract terms from an expression. Here is a polynomial in 
:
| In[6]:= |
| Out[6]= |  |
Get the coefficient of 
(the constant term):
| In[7]:= |
| Out[7]= |  |
Get the same term by replacing 
with zero, thus eliminating all terms that depend on 
:
| In[8]:= |
| Out[8]= |  |
Get the list of the monomials ordered from high to low powers of 
:
| In[9]:= |
| Out[9]= |  |
The polynomial will appear in the same order when displayed in TraditionalForm:
| In[10]:= |
Out[10]//TraditionalForm= | |
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