Difference between revisions of "If Command"

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<noinclude>{{Manual Page|version=4.2}}</noinclude>
 
<noinclude>{{Manual Page|version=4.2}}</noinclude>
 
{{command|logical}}
 
{{command|logical}}
; If[ <Condition>, <Object> ]: Yields a copy of the object if the condition evaluates to ''true'', and an undefined object if it evaluates to ''false''.
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; If[ <Condition>, <Then> ]
; 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''.
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: Yields a copy of the object ''Then'' if the condition evaluates to ''true'', and an undefined object if it evaluates to ''false''.
{{warning|Both objects '''must''' be of the same type.}}
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:{{example|1=<div><code><nowiki>If[true, x + y = 4]</nowiki></code> yields line ''x + y = 4''</div>}}
 +
; 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|1=<div>
 +
:*<code><nowiki>If[true, x + y = 4, x - y = 4]</nowiki></code> yields line ''x + y = 4''
 +
:*<code><nowiki>If[false, x + y = 4, x - y = 4]</nowiki></code> yields line ''x - y = 4''</div>}}
  
 
===Conditional Functions===
 
===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 Command|Derivative]], [[Integral Command|Integral]], and [[Intersect Command|Intersect]].
+
: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 Command|Derivative]], [[Integral Command|Integral]], and [[Intersect Command|Intersect]].
 +
:{{Examples|1=<div>
 +
:* <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>}}
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:{{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.}}
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{{note|See section: [[Boolean values]] for the symbols used in conditional statements.}}
 +
 
  
{{Examples|1=<div>
 
* <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>}}
 
{{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 in Scripting==
If command can be used in scripts to perform different actions under certain conditions.
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:If command can be used in scripts to perform different actions under certain conditions.
{{example|1= Let ''n'' be a number, and ''A'' a point. The command <code>If[Mod[n, 7] == 0, SetCoords[A, n, 0], SetCoords[A, n, 1]]</code> modifies the coordinates of point ''A'' according to the given condition. In this case it would be easier to use  <code> SetCoords[A, n, If[Mod[n, 7] == 0,0,1]]</code>.
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:{{example|1= Let ''n'' be a number, and ''A'' a point. The command <code>If[Mod[n, 7] == 0, SetCoords[A, n, 0], SetCoords[A, n, 1]]</code> modifies the coordinates of point ''A'' according to the given condition. In this case it would be easier to use  <code> SetCoords[A, n, If[Mod[n, 7] == 0,0,1]]</code>.
 
}}
 
}}
Note that arguments of If must be Objects or [[Scripting Commands]], not assignments. Syntax <code>b=If[a>1,2,3]</code> is correct, but b=2 or b=3 would not be accepted as parameters of If.
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:{{note|1= Arguments of If must be Objects or [[Scripting Commands]], not assignments. Syntax <code><nowiki>b = If[a > 1, 2, 3]</nowiki></code> is correct, but ''b = 2'' or ''b = 3'' would not be accepted as parameters of If.}}

Revision as of 13:11, 16 July 2013



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 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.
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