Difference between revisions of "If Command"
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:{{Examples|1=<div> | :{{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[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). |
+ | :* <code>f(x) =If[x<-1,x²,-1<=x<=1,1,-x²+2]</code> yields a function that equals ''x<sup>2</sup>'' for "x < -1", and 1 for ''x'' between -1 and 1 and ''- x<sup>2</sup> + 2'' otherwise). | ||
+ | </div>}} | ||
:{{note|1= A shorter syntax for this is <code>f(x) = sin(x), 0 <= x <= 3</code>}} | :{{note|1= A shorter syntax for this is <code>f(x) = sin(x), 0 <= x <= 3</code>}} | ||
:{{notes|1=<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. | :* 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>}} | :* See section: [[Boolean values]] for the symbols used in conditional statements.</div>}} | ||
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==If Command in Scripting== | ==If Command in Scripting== |
Revision as of 20:12, 5 November 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 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).f(x) =If[x<-1,x²,-1<=x<=1,1,-x²+2]
yields a function that equals x2 for "x < -1", and 1 for x between -1 and 1 and - x2 + 2 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.