Difference between revisions of "Iteration Command"

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(added v4 - example formatting)
(:<code>Iteration(a^2+1,a,{(1+ί)/(sqrt(2))},5)</code> will do a repeated iteration on a complex number)
 
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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}}
{{command|function}}
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;Iteration( <Function>, <Start Value>, <Number of Iterations> )
; Iteration[Function, Number x0, Number n]: Iterates the function ''n'' times using the given start value ''x0''.
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:Iterates the function ''n'' times (''n'' = number of iterations) using the given start value.
: {{Example| 1=After defining <code>f(x) = x^2</code> the command <code>Iteration[f, 3, 2]</code> gives you the result ''(3<sup>2</sup>)<sup>2</sup> = 81''.}}
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:{{Examples| 1=<div>
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:*After defining <code>f(x) = x^2</code> the command <code>Iteration(f, 3, 2)</code> gives you the result (3<sup>2</sup>)<sup>2</sup> = 81.
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:*''Repeated addition'': To obtain the repeated addition of 7 to the number 3, define <code>g(x) = x + 7</code>, then <code>Iteration(g, 3, 4)</code> yields (((3+7) +7) +7) +7 = 31.</div>}}
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;Iteration( <Expression>, <Variable Name>, ..., <Start Values>, <Number of Iterations> )
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:Iterates the expression ''n'' times (''n'' = number of iterations) using the given start value. The result is then the last element of the output of [[IterationList Command]], with the same parameters.
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:{{Example| 1=
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:<code>Iteration(a^2+1,a,{(1+ί)/(sqrt(2))},5)</code> will do a repeated iteration on a complex number
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}}
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{{Note|See [[IterationList Command]] for further details.}}

Latest revision as of 22:24, 17 July 2018


Iteration( <Function>, <Start Value>, <Number of Iterations> )
Iterates the function n times (n = number of iterations) using the given start value.
Examples:
  • After defining f(x) = x^2 the command Iteration(f, 3, 2) gives you the result (32)2 = 81.
  • Repeated addition: To obtain the repeated addition of 7 to the number 3, define g(x) = x + 7, then Iteration(g, 3, 4) yields (((3+7) +7) +7) +7 = 31.


Iteration( <Expression>, <Variable Name>, ..., <Start Values>, <Number of Iterations> )
Iterates the expression n times (n = number of iterations) using the given start value. The result is then the last element of the output of IterationList Command, with the same parameters.
Example: :Iteration(a^2+1,a,{(1+ί)/(sqrt(2))},5) will do a repeated iteration on a complex number
Note: See IterationList Command for further details.
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