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Defining VariablesManipulating Elements of Lists

1.2.3 Making Lists of Objects

In doing calculations, it is often convenient to collect together several objects, and treat them as a single entity. Lists give you a way to make collections of objects in Mathematica. As you will see later, lists are very important and general structures in Mathematica.

A list such as {3, 5, 1} is a collection of three objects. But in many ways, you can treat the whole list as a single object. You can, for example, do arithmetic on the whole list at once, or assign the whole list to be the value of a variable.

Here is a list of three numbers.

In[1]:= {3, 5, 1}

Out[1]=

This squares each number in the list, and adds 1 to it.

In[2]:= {3, 5, 1}^2 + 1

Out[2]=

This takes differences between corresponding elements in the two lists. The lists must be the same length.

In[3]:= {6, 7, 8} - {3.5, 4, 2.5}

Out[3]=

The value of % is the whole list.

In[4]:= %

Out[4]=

You can apply any of the mathematical functions in Section 1.1.3 to whole lists.

In[5]:= Exp[ % ] // N

Out[5]=

Just as you can set variables to be numbers, so also you can set them to be lists.

This assigns v to be a list.

In[6]:= v = {2, 4, 3.1}

Out[6]=

Wherever v appears, it is replaced by the list.

In[7]:= v / (v - 1)

Out[7]=

Defining VariablesManipulating Elements of Lists