This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / Built-in Functions / Programming / Functional Programming /

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]:=