Mathematica Cookbook

Chapter 1. Numerics

Jenny I’ve got your number I need to make you mine Jenny don’t change your number Eight six seven five three oh nine Eight six seven five three oh nine Eight six seven five three oh nine Eight six seven five three oh nine

—Tommy Tutone, “867-5309/Jenny”

1.0 Introduction

Numerical Types

Mathematics is a huge, almost all-encompassing subject, and the average layperson often fails to appreciate the types of exotic objects that are in the mathematician’s domain. Yet every person on the street perceives math is about numbers. So even though numbers only scratch the surface of math and Mathematica, it makes sense to begin with their representation.

Mathematica supports four numerical types: Integer, Rational, Real, and Complex. In the following examples we use Mathematica’s comment notation ( *comment* ).

1         (*The integer one*)
1 / 2     (*The rational one half*)
1.2 * ^ 8 (*The real 1.2 x 10^8*)
3 + 2 I   (*The complex number 3+2i*)

There is no need to take my word that these expressions have the specified types. You can ask Mathematica to tell you using the function Head[] , which returns the head of an expression (i.e., head of a list).

In[2]:=  Head[1]
Out[2]=  Integer

In[3]:=  Head[1/2]
Out[3]=  Rational

In[4]:=  Head[1.2 ^ 8]
Out[4]=  Real

In[5]:=  Head[3 + 2 I]
Out[5]=  Complex

Although Mathematica does not internally store numbers as lists, it provides the illusion that a number has a head indicating its type. This is consistent with the fact that everything in Mathematica ...