# Difference between revisions of "If Command"

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− | <noinclude>{{Manual Page | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}} |

− | {{command|logical}} | + | ; If( <Condition>, <Then> ) |

− | ; If | + | : Yields a copy of the object ''Then'' if the condition evaluates to ''true'', and an undefined object if it evaluates to ''false''. |

− | ; If | + | :{{Examples|1=<div> |

− | < | + | :*Let ''n'' = 3. <code><nowiki>If(n==3, x + y = 4)</nowiki></code> yields line ''x'' + ''y'' = 4, because the condition on number ''n'' is met. |

− | + | :*Let ''n'' = 4. <code><nowiki>If(n==3, x + y = 4)</nowiki></code> creates an ''undefined'' object, because the condition on number ''n'' is not met .</div>}} | |

− | * | + | ; If( <Condition>, <Then>, <Else> ) |

− | * See | + | : 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|1= Let ''n'' be a number. <code><nowiki>If(n==3, x + y = 4, x - y = 4)</nowiki></code> yields line ''x'' + ''y'' = 4 when ''n'' = 3, and line ''x'' - ''y'' = 4 for all ''n'' not equal to 3.}} |

+ | ; If( <Condition 1>, <Then 1>, <Condition 2>, <Then 2>, ... , <Else (optional)> ) | ||

+ | : Yields a copy of "Then 1" when first condition is satisfied, "Then 2" if second condition is satisfied etc. If none of the conditions are satisfied and Else is given, this command yields a copy of Else. Otherwise undefined is returned. | ||

+ | :{{example| 1=<code>If(a ≟ 1, "Matthew", a ≟ 2,"Larry", a ≟ 3, "Vivian", "Alex")</code> When ''a''=1 this returns the text "Matthew", for ''a''=2' it returns "Larry", for ''a''=3 "Vivian" and for all other values of ''a'' it yields "Alex".}} | ||

+ | |||

+ | ===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]]. | ||

+ | :{{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). | ||

+ | ::{{note|1= A shorter syntax for this is <code>f(x) = sin(x), 0 <= x <= 3</code>}} | ||

+ | :* <code>f(x) =If(x<-1,x²,-1<=x<=1,1,-x²+2)</code> yields the piecewise function <math>f(x) = \left\{\begin{matrix}{} x^{2}& : &x < -1\\ 1& :& -1 ≤ x ≤ 1\\ -x^{2} + 2& : &\text{otherwise} \end{matrix}\right </math>. | ||

+ | </div>}} | ||

+ | |||

+ | |||

+ | :{{notes|1=<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. | ||

+ | :* See section: [[Boolean values]] for the symbols used in conditional statements.</div>}} | ||

+ | |||

+ | ==If Command in Scripting== | ||

+ | :'''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>.}} | ||

+ | :{{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'''.}} |

## Latest revision as of 10:59, 15 July 2018

- 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

- 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.

- If( <Condition 1>, <Then 1>, <Condition 2>, <Then 2>, ... , <Else (optional)> )
- Yields a copy of "Then 1" when first condition is satisfied, "Then 2" if second condition is satisfied etc. If none of the conditions are satisfied and Else is given, this command yields a copy of Else. Otherwise undefined is returned.
**Example:**`If(a ≟ 1, "Matthew", a ≟ 2,"Larry", a ≟ 3, "Vivian", "Alex")`

When*a*=1 this returns the text "Matthew", for*a*=2' it returns "Larry", for*a*=3 "Vivian" and for all other values of*a*it yields "Alex".

### 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*for^{2}*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`

`f(x) =If(x<-1,x²,-1<=x<=1,1,-x²+2)`

yields the piecewise function f(x) = \left\{\begin{matrix}{} x^{2}& : &x < -1\\ 1& :& -1 ≤ x ≤ 1\\ -x^{2} + 2& : &\text{otherwise} \end{matrix}\right .

**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.

- Derivative of

## 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**.