If Command

If[ <Condition>, <Then> ]

Yields a copy of the object Then if the condition evaluates to true, and an undefined object if it evaluates to false.

Example:

If[true, x + y = 4] yields line x + y = 4

If[ <Condition>, <Then>, <Else> ]

Yields a copy of object Then if the condition evaluates to true, and a copy of object Else if it evaluates to false.

Warning:

Both objects must be of the same type.

Example:

• If[true, x + y = 4, x - y = 4] yields line x + y = 4
• If[false, x + y = 4, x - y = 4] yields line x - y = 4

Conditional Functions

The If command can be used to create conditional functions. Such conditional functions may be used as arguments in any command that takes a function argument, such as Derivative, Integral, and Intersect.

Examples:

• f(x) = If[x < 3, sin(x), x^2] yields a piecewise function that equals sin(x) for x < 3 and x² for x ≥ 3.
• f(x) = If[0 <= x <= 3, sin(x)] yields a function that equals sin(x) for x between 0 and 3 (and undefined otherwise).

Note: Derivative of If[condition, f(x), g(x)] gives If[condition, f'(x), g'(x)]. It does not do any evaluation of limits at the critical points.

Note: See section: Boolean values for the symbols used in conditional statements.

If Command in Scripting

If command can be used in scripts to perform different actions under certain conditions.

Example: Let n be a number, and A a point. The command If[Mod[n, 7] == 0, SetCoords[A, n, 0], SetCoords[A, n, 1]] modifies the coordinates of point A according to the given condition. In this case it would be easier to use SetCoords[A, n, If[Mod[n, 7] == 0,0,1]].

Note: Arguments of If must be Objects or Scripting Commands, not assignments. Syntax b = If[a > 1, 2, 3] is correct, but b = 2 or b = 3 would not be accepted as parameters of If.