Variables, Equations, and Expressions

Maple variables are names that generally begin with a letter and are
followed by up to 498 alphanumeric or underscore characters; case is
significant (eg: x is different from X in Maple).  Maple distinguishes
between two kinds of variables.  A Maple programming variable is a
variable that you have assigned a result to, generally with an
assignment statement:

> x := 2 + 5;
x := 7
> x;
7

The programming variable x now is a label for the result of 2+5.

The other kind of Maple variable is a mathematical variable or an
unassigned variable.  These exist in the sense of algebraic unknowns, as
in the case of:

> z := 2+y;
z := 2 + y

Here, y is a mathematical variable, and z is a programming variable
because an expression has been assigned to it.  If we now assign a value
to y, y becomes a programming variable, and is no longer an algebraic
unknown:

> y := 5;
y := 5
> z;
7

An equation is different from an assignment statement.  Consider the
difference between:

> a := 2;
a := 2;
> b = 2;
b = 2

In the first case we are assigning the value 2 to the variable a.  In
the second case, we are making the assertion that b is in fact already
equal to 2.  We can evaluate the boolean assertion using the evalb
function:

> # First, see what the value of b is:
> b;
b
> # So b is a mathematical variable.  Try the evaluation:
> evalb(b=2);
false
> # Now assign the value 2 to b:
> b := 2;
b := 2
> b;
2
> # So b is now a programming variable.  Evaluate the assertion again:
> evalb(b=2);
true
> # Now assign the assertion to a (which replaces the old contents of a):
> a := b = 2;
a := 2 = 2
> evalb(a);
true

The last part of the example shows that you can assign an expression to
a variable.  Maple statements are built of zero or more expressions of
various types connected in various ways.  Thus b=2, and abs(4) are both
expressions, while evalb(b=2) is a composite expression built from
evalb(...) and b=2.  Finally, evalb(b=2) and (c = 3); is a statement,
because it is built from (boolean) expressions and is terminated.