Difference between revisions of "If Command"
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:* <code>f(x) = If[x < 3, sin(x), x^2]</code> yields a piecewise function that equals ''sin(x)'' for ''x < 3'' and ''x<sup>2</sup>'' for ''x ≥ 3''.  :* <code>f(x) = If[x < 3, sin(x), x^2]</code> yields a piecewise function that equals ''sin(x)'' for ''x < 3'' and ''x<sup>2</sup>'' for ''x ≥ 3''.  
:* <code>f(x) = If[0 <= x <= 3, sin(x)]</code> yields a function that equals ''sin(x)'' for x between 0 and 3 (and undefined otherwise).</div>}}  :* <code>f(x) = If[0 <= x <= 3, sin(x)]</code> yields a function that equals ''sin(x)'' for x between 0 and 3 (and undefined otherwise).</div>}}  
+  :{{note1= A shorter syntax for this is <code>f(x) = sin(x), 0 <= x <= 3</code>}}  
:{{notes1=<div>  :{{notes1=<div>  
:* 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.  :* 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. 
Revision as of 10:08, 24 July 2015
 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.
 Examples:
 Let n = 3.
If[n==3, x + y = 4]
yields line x + y = 4, because the condition on number n is met.  Let n = 4.
If[n==3, x + y = 4]
creates an undefined object, because the condition on number n is not met .
 Let n = 3.
 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. Both objects must be of the same type.
 Example: Let n be a number.
If[n==3, x + y = 4, x  y = 4]
yields line x + y = 4 when n = 3, and line x  y = 4 for all n not equal to 3.
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 x^{2} 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: A shorter syntax for this is
f(x) = sin(x), 0 <= x <= 3
 Notes:
 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.
 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 useSetCoords[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.