The difference between = and :=

Recall that Maple uses := as the assignment operator. Thus a statement like x := 3 actually sets x equal to 3 and Maple will then substitute in 3 every time it sees the variable x, until you set x equal to something else. This is in contrast to the equal operator = (no colon). The "=" operator is a comparison operator used when setting up equations. Here's an example. First, let's consider the expression

> x := 3;

This actually sets x equal to 3. If you ask Maple what x or x squared is:

> x; x^2;

Contrast this to using "=" with no colon:

> y = 3;

This did NOT set y equal to 3. You can check by asking Maple what it thinks y is:

> y;

The expression y = 3 is an equation, waiting around to be solved or otherwise manipulated. The difference between
y := 3 and y = 3 might roughly be translated into plain English as follows. To tell Maple y := 3 means "Set y equal to 3", while telling Maple y = 3 is like saying "what if y was equal to 3?"

As another example, you can sensibly combine ":=" and "=" in one expression. Suppose we want to construct the equation [Maple Math] . You can do this with the expression

> 6*y - 2 = 0;

At times it's advantageous to actually name equations. Suppose we want to name the above equation " eqn ". We do this by assigning " eqn " to be the equation [Maple Math] ,

> eqn := 6*y - 2 = 0;

You can now refer to the equation [Maple Math] by just typing the name,

> eqn;

or solve it:

> solve(eqn, y);


This illustrates that one can assign a variable to be any value (in this case, an equation), not just a number. If the difference between ":=" and "=" seems confusing, just remember for now to use ":=" when you actually want to assign a value to some variable and "=" when you set up equations to solve.