If Command

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If[ <Condition>, <Object> ]
Yields a copy of the object if the condition evaluates to true, and an undefined object if it evaluates to false.
If[ <Condition>, <Object a>, <Object b> ]
Yields a copy of object a if the condition evaluates to true, and a copy of object b if it evaluates to false.
Warning Warning: Both objects must be of the same type.

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.

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

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 that 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.
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