Difference between revisions of "Min Command"
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m (change Min[ x^3 + 2x^2 - 1, -2, 0] to Min[ x^3 + 2x^2 - 1, -2, 1]) |
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|algebra}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|algebra}} | ||
| − | ;Min | + | ;Min( <List> ) |
:Returns the minimum of the numbers within the list. | :Returns the minimum of the numbers within the list. | ||
| − | :{{example| 1=<code><nowiki>Min | + | :{{example| 1=<code><nowiki>Min({-2, 12, -23, 17, 15})</nowiki></code> yields ''-23''.}} |
| − | :{{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 | + | :{{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( <List> ) will yield the minimum segment length.}} |
| − | ;Min | + | ;Min( <Interval> ) |
:Returns the lower bound of the interval. | :Returns the lower bound of the interval. | ||
| − | :{{example| 1=<code><nowiki>Min | + | :{{example| 1=<code><nowiki>Min(2 < x < 3)</nowiki></code> yields ''2'' .}} |
| − | :{{note| 1= | + | :{{note| 1=Open and closed intervals are not distinguished.}} |
| − | ;Min | + | ;Min( <Number>, <Number> ) |
:Returns the minimum of the two given numbers. | :Returns the minimum of the two given numbers. | ||
| − | :{{example| 1=<code><nowiki>Min | + | :{{example| 1=<code><nowiki>Min(12, 15)</nowiki></code> yields ''12''.}} |
| − | ;Min | + | ;Min( <Function>, <Start x-Value>, <End x-Value> ) |
| − | :Calculates (numerically) the minimum point for function in the given interval. Function should be continuous and have only one ''local'' minimum point in the interval. | + | :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. |
| − | :{{example| 1=<code><nowiki>Min | + | :{{note| 1=For polynomials you should use the [[Extremum Command]].}} |
| − | ;Min | + | :{{example| 1=<code><nowiki>Min(exp(x) x^3,-4,-2)</nowiki></code> creates the point (-3, -1.34425) .}} |
| + | ;Min( <List of Data>, <List of Frequencies> ) | ||
:Returns the minimum of the list of data with corresponding frequencies. | :Returns the minimum of the list of data with corresponding frequencies. | ||
| − | :{{example| 1=<code><nowiki>Min | + | :{{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.}} |
| − | {{note| 1=See also [[Max Command]], [[Extremum Command]] and [[Function Inspector Tool]].}} | + | {{note| 1=<div> |
| + | * 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> | ||
| + | * See also [[Max Command]], [[Extremum Command]] and [[Function Inspector Tool]].</div>}} | ||
Revision as of 09:07, 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:
- If you want the minimum of two functions
f(x)andg(x)then you can define(f(x) + g(x) - abs(f(x) - g(x)))/2 - See also Max Command, Extremum Command and Function Inspector Tool.
