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 ...