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2.4.4 Special Forms of Assignment
Particularly when you write procedural programs in Mathematica, you will often need to modify the value of a particular variable repeatedly. You can always do this by constructing the new value and explicitly performing an assignment such as x=value. Mathematica, however, provides special notations for incrementing the values of variables, and for some other common cases.
Modifying values of variables.
This assigns the value 7x to the variable t.
In[1]:= t = 7x
Out[1]= 
This increments the value of t by 18x.
In[2]:= t += 18x
Out[2]= 
The value of t has been modified.
In[3]:= t
Out[3]= 
This sets t to 8, multiplies its value by 7, then gives the final value of t.
In[4]:= t = 8; t *= 7; t
Out[4]= 
The value of i++ is the value of ibefore the increment is done.
In[5]:= i=5; Print[i++]; Print[i]
5
6
The value of ++i is the value of iafter the increment.
In[6]:= i=5; Print[++i]; Print[i]
6
6
Assigning values to several variables at a time.
This assigns the value 5 to x and 8 to y.
In[7]:= {x, y} = {5, 8}
Out[7]= 
This interchanges the values of x, y.
In[8]:= {x, y} = {y, x}
Out[8]= 
Now x has value 8.
In[9]:= x
Out[9]= 
And y has value 5.
In[10]:= y
Out[10]= 
You can use assignments to lists to permute values of variables in any way.
In[11]:= {a, b, c} = {1, 2, 3}; {b, a, c} = {a, c, b}; {a, b, c}
Out[11]= 
When you write programs in Mathematica, you will sometimes find it convenient to take a list, and successively add elements to it. You can do this using the functions PrependTo and AppendTo.
Assignments for modifying lists.
This assigns the value of v to be the list {5,7,9}.
In[12]:= v = {5, 7, 9}
Out[12]= 
This appends the element 11 to the value of v.
In[13]:= AppendTo[v, 11]
Out[13]= 
Now the value of v has been modified.
In[14]:= v
Out[14]= 
Although AppendTo[v,elem] is always equivalent to v=Append[v,elem], it is often a convenient notation. However, you should realize that because of the way Mathematica stores lists, it is usually less efficient to add a sequence of elements to a particular list than to create a nested structure that consists, for example, of lists of length 2 at each level. When you have built up such a structure, you can always reduce it to a single list using Flatten.
This sets up a nested list structure for w.
In[15]:= w = {1}; Do[ w = {w, k^2}, {k, 1, 4} ]; w
Out[15]= 
You can use Flatten to unravel the structure.
In[16]:= Flatten[w]
Out[16]= 
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