1.4.6 Simplifying Algebraic Expressions

80 1. A Practical Introduction to Mathematica
1.4.6 Simplifying Algebraic Expressions
There are many situations where you want to write a particular algebraic expression
in the \simplest possible form". Although it is dicult to know exactly what one
means in all cases by the \simplest form", a worthwhile practical procedure is to
look at many dierent forms of an expression, and pick out the one that involves
the smallest number of parts.
Simplify[expr]
try to nd the form of expr with the smallest number
of parts, by applying a sequence of dierent algebraic
transformations
Simplifying algbraic expressions.
Simplify writes x 2 +2x + 1 in factored
form.
In[1]:= Simplify[x^2 + 2x + 1]
2
Out[1]= (1 + x)
Simplify leaves x 10 ; 1 in expanded form,
since for this expression, the factored form
is larger.
In[2]:= Simplify[x^10 -1]
10
Out[2]= -1 + x
You can often use Simplify to \clean up" complicated expressions that you get
as the results of computations.
1
Here is the integral of
x 4 . Integrals are
;1
discussed in more detail in Section 1.5.
In[3]:= Integrate[1/(x^4-1), x]
-ArcTan[x] Log[-1 + x] Log[1 + x]
Out[3]= ------------------ + ------------------ - ------------------
2 4 4
Dierentiating the result from Integrate
should give back your original expression.
In this case, as is common, you get a more
complicated version of the expression.
In[4]:= D[%, x]
1 1 1
Out[4]= ------------------ - ---------------- - -------------------
4 (-1 + x) 4 (1 + x) 2
2 (1 + x )
Simplify succeeds in getting back the
original, more simple, form of the
expression.
In[5]:= Simplify[%]
1
Out[5]= ------------
4
-1 + x
For many simple algebraic calculations, you may nd it convenient to use
Simplify quite routinely on your results.
In more complicated calculations, however, you often need to exercise more con-
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1.4 Formulae 81
trol over the exact form of answer that you get. In addition, when your expressions
are complicated, Simplify may spend a long time testing a large number of possible
forms, in its attempt to nd the simplest one.
Web sample page from The Mathematica Book, First Edition, by Stephen Wolfram, published by Addison-Wesley Publishing
Company (hardcover ISBN 0-201-19334-5; softcover ISBN 0-201-19330-2). To order Mathematica or this book contact Wolfram
Research: info@wolfram.com; http://www.wolfram.com/; 1-800-441-6284.
c 1988 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their
personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly
prohibited.