Set a value for :

Now use it:

Unset :

Set multiple values:

Evaluate an expression using those set values:

Set and to the same value:

Check:

Set and to different values:

Interchange values:

Check that they were swapped:

A sparse array:

Set a part:

v is still a sparse array, with its second part changed:

Assign multiple return values of a function to individual variables:

See the results:

A definition for a pattern with a specific head is associated with that head:

Show the definition:

Evaluate with it:

Compute the GCD of two numbers:

Find a fixed point:

Compute using Newton's method:

Use a variable as an abbreviation for a complicated expression used more than once:

A scalar implementation of backsubstitution in a system of linear equations:

A vector implementation of backsubstitution in a system of linear equations:

The right side of an immediate definition is evaluated when the definition is made:

Multiple copies are the same value:

The right side of a delayed definition is evaluated each time the definition is used:

Now it evaluates three different times:

The arguments of the left side of a definition are evaluated before the definition is made:

Definitions with the same left side overwrite earlier ones:

Redefine:

See that it has the new value:

Make definitions for special and general cases using immediate and delayed assignments:

More specific definitions are put in front of more general ones:

Use this definition of fact:

The pattern variable is renamed if necessary inside a nested scope:

Inspect it:

Use it:

Module introduces new symbols, distinct from global ones:

Check that the global value of x is retained:

Set a value for a:

Definition prints definitions associated with a symbol:

Information prints various information about a symbol, including any definitions:

OwnValues returns a list of rules corresponding to any downvalues defined:

Define a function fact to compute factorials:

Use Unset (=.) to clear definitions with a particular left-hand side:

Check that the cleared definition is no longer present:

Clear all definitions:

In the presence of global variables, pattern variables may show unexpected behavior:

Using a non-delayed assignment means the right side is evaluated before Set is done:

So the evaluation uses the global setting and not the actual input to f:

Delayed assignments behave as expected:

Check that the value 2 is used and not the global value of 5:

Runaway definitions:

Setting an initial value avoids this:

Pattern variables are not symbols; you cannot normally assign to them:

Use local variables for this purpose:

Use upvalues to assign to subscripted variables:

Subscripted variables are distinct from indexed variables:

Compute the arithmetic-geometric mean of two numbers [more info]: