Difference between revisions of "Min Command"

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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|cas=true|algebra}}
{{command|algebra}}
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;Min( <List> )
; Min[Number a, Number b]: Yields the minimum of the given numbers ''a'' and ''b''.
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:Returns the minimum of the numbers within the list.
; Min[List of Numbers]: Yields the minimum of the numbers within the list.
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:{{example| 1=<code><nowiki>Min({-2, 12, -23, 17, 15})</nowiki></code>  yields ''-23''.}}
{{Note|If the input consists of non-numeric objects, then Min[] considers the numbers associated with those objects. For example, Min[List of Segments] will yield the minimum segment length.}}
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:{{note| 1=If the input consists of non-numeric objects, then this command considers the numbers associated with those objects. If you have a list of segments for example, the command Min( &lt;List> ) will yield the minimum segment length.}}
;Min[ <Function>, <left-x>, <right-x> ]
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;Min( <Interval> )
:Calculates the minimum point for function in the given interval. Function should only have one minimum point in the interval.
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:Returns the lower bound of the interval.
{{Note|See also [[Extremum Command]] and [[Function Inspector Tool]].}}
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:{{example| 1=<code><nowiki>Min(2 < x < 3)</nowiki></code> yields ''2'' .}}
;Min[ <Interval > ]
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:{{note| 1=Open and closed intervals are not distinguished.}}
:Returns the lower bound of the interval, e.g. <code>Min[2<x<3]</code> returns 2. It is the same for open and closed intervals.
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;Min( <Number>, <Number> )
==CAS Syntax==
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:Returns the minimum of the two given numbers.
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:{{example| 1=<code><nowiki>Min(12, 15)</nowiki></code>  yields ''12''.}}
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;Min( <Function>, <Start x-Value>, <End x-Value> )
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:Calculates (numerically) the '''local''' minimum point for function in the given interval. Function should be continuous and have only one ''local'' minimum point in the interval.  
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:{{note| 1=For polynomials you should use the [[Extremum Command]].}}
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:{{example| 1=<code><nowiki>Min(exp(x) x^3,-4,-2)</nowiki></code> creates the point (-3, -1.34425) .}}
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;Min( <List of Data>, &lt;List of Frequencies> )
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:Returns the minimum of the list of data with corresponding frequencies.  
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:{{example| 1=<code><nowiki>Min({1, 2, 3, 4, 5}, {0, 3, 4, 2, 3})</nowiki></code> yields 2, the lowest number of the first list whose frequency is greater than 0.}}
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{{note| 1=<div>
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* If you want the minimum of two functions <code>f(x)</code> and <code>g(x)</code> then you can define <code>(f(x) + g(x) - abs(f(x) - g(x)))/2</code>
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* See also [[Max Command]], [[Extremum Command]] and [[Function Inspector Tool]].</div>}}

Revision as of 08:07, 25 October 2019


Min( <List> )
Returns the minimum of the numbers within the list.
Example: Min({-2, 12, -23, 17, 15}) yields -23.
Note: If the input consists of non-numeric objects, then this command considers the numbers associated with those objects. If you have a list of segments for example, the command Min( <List> ) will yield the minimum segment length.
Min( <Interval> )
Returns the lower bound of the interval.
Example: Min(2 < x < 3) yields 2 .
Note: Open and closed intervals are not distinguished.
Min( <Number>, <Number> )
Returns the minimum of the two given numbers.
Example: Min(12, 15) yields 12.
Min( <Function>, <Start x-Value>, <End x-Value> )
Calculates (numerically) the local minimum point for function in the given interval. Function should be continuous and have only one local minimum point in the interval.
Note: For polynomials you should use the Extremum Command.
Example: Min(exp(x) x^3,-4,-2) creates the point (-3, -1.34425) .
Min( <List of Data>, <List of Frequencies> )
Returns the minimum of the list of data with corresponding frequencies.
Example: Min({1, 2, 3, 4, 5}, {0, 3, 4, 2, 3}) yields 2, the lowest number of the first list whose frequency is greater than 0.


Note:
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