This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 Further Examples: Apply (@@) This substitutes New for Old at the head of the expression using the shorthand notation for Apply. (Neither New nor Old has a built-in meaning in Mathematica.) In[1]:= Out[1]= This is the same thing. In[2]:= Out[2]= The head of a product is Times. In[3]:= Out[3]= The head of a list is List. In[4]:= Out[4]= You can see heads explicitly using FullForm. In[5]:= Out[5]//FullForm= In[6]:= Out[6]//FullForm= This substitutes Times for List. In[7]:= Out[7]= This changes a line into a polygon. In[8]:= Out[8]= This constructs a list of circles from a list of pairs of centers and radii. In[9]:= Out[9]= Here is another way to write the previous expression. In[10]:= Out[10]= Here, Apply replaces heads in subexpressions at level . In[11]:= Out[11]= Here is a list. In[12]:= This defines a function ff that permutes mm. In[13]:= The permutation can be written as a list of ordered pairs. In[14]:= Out[14]= Another way to write the permutation is as a list of rules. In[15]:= Out[15]= These rules can be represented more compactly as a list of cycles. In[16]:= This defines the function CyclesfromRules that finds all cycles from a list of rules. In[17]:= In[18]:= In[19]:= Here are the cycles of ff using CyclesfromRules. In[20]:= Out[20]= In[21]:=