6.7 Advanced Topic: Putting Expressions into Different Forms
Complicated algebraic expressions can usually be written in many different ways. Mathematica TE provides a variety of functions for converting expressions from one form to another.
In most applications, the most common of these functions are Expand, Factor and Simplify. However, particularly when you have rational expressions that contain quotients, you may need to use other functions.
Functions for transforming algebraic expressions.
Here is a rational expression that can be written in many different forms.
In[1]:= e = (x - 1)^2 (2 + x) / ((1 + x) (x - 3)^2)
Out[1]= 
ExpandDenominator expands out the denominator.
In[2]:= ExpandDenominator[e]
Out[2]= 
ExpandNumerator writes the numerator in expanded form.
In[3]:= ExpandNumerator[e]
Out[3]= 
Expand expands out the numerator, but leaves the denominator in factored form.
In[4]:= Expand[e]
Out[4]= 
ExpandAll expands out everything, including the denominator.
In[5]:= ExpandAll[e]
Out[5]= 
Together collects all the terms together over a common denominator.
In[6]:= Together[%]
Out[6]= 
Apart breaks the expression apart into terms with simple denominators. In mathematical terms, Apart decomposes a rational expression into "partial fractions".
In[7]:= Apart[%]
Out[7]= 
Factor factors everything, in this case reproducing the original form.
In[8]:= Factor[%]
Out[8]= 
Getting expressions into the form you want is something of an art. In most cases, it is best simply to experiment, trying different transformations until you get what you want.
Other Mathematica functions related to polynomials. (See Section 3.2.)
