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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}


  • This squares each number in the list, and adds 1 to it.
  • In[2]:= {3, 5, 1}^2 + 1


  • 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}


  • The value of % is the whole list.
  • In[4]:= %


  • You can apply any of the mathematical functions in Section 1.1.3 to whole lists.
  • In[5]:= Exp[ % ] // N


    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}


  • Wherever v appears, it is replaced by the list.
  • In[7]:= v / (v - 1)