# Defining Variables

When you do long calculations, it is often convenient to give *names* to your intermediate results. Just as in standard mathematics, or in other computer languages, you can do this by introducing named *variables*.

This sets the value of the

*variable* to be

.

Out[1]= | |

Whenever

appears,

*Mathematica* now replaces it with the value

.

Out[2]= | |

This assigns a new value to

.

Out[3]= | |

is set to be the numerical value of

to 40-digit accuracy.

Out[4]= | |

Here is the value you defined for

.

Out[5]= | |

This gives the numerical value of

, to the same accuracy as

.

Out[6]= | |

x=value | assign a value to the variable x |

x=y=value | assign a value to both x and y |

x=. or Clear[x] | remove any value assigned to x |

Assigning values to variables.

It is very important to realize that values you assign to variables are *permanent*. Once you have assigned a value to a particular variable, the value will be kept until you explicitly remove it. The value will, of course, disappear if you start a whole new *Mathematica* session.

Forgetting about definitions you made earlier is the single most common cause of mistakes when using *Mathematica*. If you set , *Mathematica* assumes that you *always* want to have the value , until or unless you explicitly tell it otherwise. To avoid mistakes, you should remove values you have defined as soon as you have finished using them.

• Remove values you assign to variables as soon as you finish using them. |

A useful principle in using *Mathematica*.

The variables you define can have almost any name. There is no limit on the length of their names. One constraint, however, is that variable names can never *start* with numbers. For example, could be a variable, but means .

*Mathematica* uses both uppercase and lowercase letters. There is a convention that built-in *Mathematica* objects always have names starting with uppercase (capital) letters. To avoid confusion, you should always choose names for your own variables that start with lowercase letters.

aaaaa | a variable name containing only lowercase letters |

Aaaaa | a built-in object whose name begins with a capital letter |

Naming conventions.

You can type formulas involving variables in *Mathematica* almost exactly as you would in mathematics. There are a few important points to watch, however.

• means times . |

• with no space is the variable with name . |

• means times . |

• means , not . |

Some points to watch when using variables in *Mathematica*.