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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 i before the increment is done.

In[5]:= i=5; Print[i++]; Print[i]

The value of ++i is the value of i after the increment.

In[6]:= i=5; Print[++i]; Print[i]

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 and 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]=

Making DefinitionsMaking Definitions for Indexed Objects