Difference between revisions of "Min Command"

Latest revision as of 13:43, 22 November 2023

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 (and no local maximum).; 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) and g(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.

CAS Syntax

Min( <Function>, <Start x-Value>, <End x-Value> )

Unlike in the Algebra View, this syntax will give the minimum over the interval, including endpoints

Example:

Min(x^2,-1,2) yields the point (0,0)
Min(-x^2,-1,2) yields the point (2,-4)

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|algebra}}
-{{command|algebra}}
+;Min( <List> )
-; Min[Number a, Number b]: Yields the minimum of the given numbers ''a'' and ''b''.
+:Returns the minimum of the numbers within the list.
-; Min[List of Numbers]: Yields the minimum of the numbers within the list.
+:{{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.}}
+:{{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> ]
+;Min( <Interval> )
-:Calculates the minimum point for function in the given interval. Function should only have one minimum point in the interval.
+:Returns the lower bound of the interval.
-{{Note|See also [[Extremum Command]] and [[Function Inspector Tool]].}}
+:{{example| 1=<code><nowiki>Min(2 < x < 3)</nowiki></code> yields ''2'' .}}
-;Min[ <Interval > ]
+:{{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.
+;Min( <Number>, <Number> )
-==CAS Syntax==
+:Returns the minimum of the two given numbers.
-; Min[Number a, Number b]: Yields the minimum of the given numbers ''a'' and ''b''.
+:{{example| 1=<code><nowiki>Min(12, 15)</nowiki></code>  yields ''12''.}}
-; Min[List of Numbers]: Yields the minimum of the numbers within the list.
+;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 (and no local maximum).
+:{{note| 1=For polynomials you should use the [[Extremum Command]].}}
+:{{example| 1=<code><nowiki>Min(exp(x) x^3,-4,-2)</nowiki></code> creates the point (-3, -1.34425) .}}
+;Min( <List of Data>, &lt;List of Frequencies> )
+:Returns the minimum of the list of data with corresponding frequencies.
+:{{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=<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>}}
-<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
-{{command|algebra}}
-;Min[Number a, Number b]
-:Yields the minimum of the given numbers ''a'' and ''b''.
-:{{example| 1=<div><code><nowiki>Min[12, 15]</nowiki></code>  yields ''12''.</div>}}
-;Min[List of Numbers]
-:Yields the minimum of the numbers within the list.
-:{{example| 1=<div><code><nowiki>Min[{-2, 12, -23, 17, 15}]</nowiki></code>  yields ''-23''.</div>}}
-{{note| 1=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.}}
-;Min[ Function, left-x, right-x ]
-:Calculates the minimum point for function in the given interval. Function should only have on minimum point in the interval.
-{{note|See also [[Extremum Command]] and [[Function Inspector Tool]].}}
-;Min[ <Interval> ]
-: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.
 ==CAS Syntax==
-;Min[Number a, Number b]
+;Min( <Function>, <Start x-Value>, <End x-Value> )
-:Yields the minimum of the given numbers ''a'' and ''b''.
+:Unlike in the Algebra View, this syntax will give the minimum over the interval, including endpoints
-:{{example| 1=<div><code><nowiki>Min[12, 15]</nowiki></code>  yields ''12''.</div>}}
+:{{example|1=<div>
-;Min[List of Numbers]
+:*<code><nowiki>Min(x^2,-1,2)</nowiki></code> yields the point ''(0,0)''
-:Yields the minimum of the numbers within the list.
+:*<code><nowiki>Min(-x^2,-1,2)</nowiki></code> yields the point ''(2,-4)''
-:{{example| 1=<div><code><nowiki>Min[{-2, 12, -23, 17, 15}]</nowiki></code>  yields ''-23''.</div>}}
+</div>}}

Difference between revisions of "Min Command"

Latest revision as of 13:43, 22 November 2023

Min

Command Categories (All commands)

CAS Syntax