https://wiki.geogebra.org/s/zh/api.php?action=feedcontributions&user=Jackhu&feedformat=atomGeoGebra Manual - 用户贡献 [zh]2024-03-28T22:05:23Z用户贡献MediaWiki 1.35.1https://wiki.geogebra.org/s/zh/index.php?title=SampleSDY_%E6%8C%87%E4%BB%A4&diff=4453SampleSDY 指令2011-10-20T01:35:25Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|SampleSDY}}<br />
;SampleSDY[ <List of Points> ]<br />
:{{translate|SampleSDY Command}}<br />
;SampleSDY[ <List of Points> ]<br />
:Returns [[w:Standard_deviation#Estimation|sample standard deviation]] of y-coordinates of [[Points and Vectors|points]] from the given [[Lists|list]].</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=SampleSDX_%E6%8C%87%E4%BB%A4&diff=4452SampleSDX 指令2011-10-20T01:34:55Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|SampleSDX}}<br />
;SampleSDX[ <List of Points> ]<br />
:{{translate|SampleSDX Command}}<br />
;SampleSDX[ <List of Points> ]<br />
:Returns [[w:Standard_deviation#Estimation|sample standard deviation]] of x-coordinates of [[Points and Vectors|points]] from the given [[Lists|list]].</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=SampleSD_%E6%8C%87%E4%BB%A4&diff=4451SampleSD 指令2011-10-20T01:34:32Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|statistics|SampleSD}}<br />
;SampleSD[ <List of Numbers> ]<br />
:{{translate|SampleSD Command}}<br />
==CAS 視窗==<br />
<br />
;SampleSD[ <List of Numbers> ]<br />
:{{translate|SampleSD Command}}<br />
;SampleSD[ <List of Numbers> ]<br />
:Returns [[w:Standard_deviation#Estimation|sample standard deviation]] of given [[Lists|list]] of numbers.<br />
:{{example|1=<div><code><nowiki>SampleSD[{1, 2, 3}]</nowiki></code> yields ''1''.</div>}}<br />
==CAS Syntax==<br />
;SampleSD[ <List of Numbers> ]<br />
:Returns [[w:Standard_deviation#Estimation|sample standard deviation]] of given [[Lists|list]] of numbers. If the list contains undefined variables, it yields a formula for the sample standard deviation.<br />
:{{example|1=<div><code><nowiki>SampleSD[{1, 2, a}]</nowiki></code> yields <math>\frac{\sqrt{a²-3a+3&#125;}{\sqrt{3&#125;}</math>.</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Sample_%E6%8C%87%E4%BB%A4&diff=4450Sample 指令2011-10-20T01:33:42Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|statistics|Sample}}<br />
;Sample[ <List>, <Size> ]<br />
:{{translate|Sample Command}}<br />
;Sample[ <List>, <Size>, <With Replacement> ]<br />
:{{translate|Sample Command}}<br />
==CAS 視窗==<br />
<br />
;Sample[ <List>, <Size> ]<br />
:{{translate|Sample Command}}<br />
;Sample[ <List>, <Size>, <With Replacement> ]<br />
:{{translate|Sample Command}}<br />
;Sample[ <List L>, <Size n> ]<br />
:Returns list of ''n'' randomly chosen elements of ''L''; elements can be chosen several times.<br />
:{{example|1=<div><code><nowiki>Sample[{1, 2, 3, 4, 5}, 5]</nowiki></code> yields for example ''{1, 2, 1, 5, 4}''.</div>}}<br />
;Sample[ <List L>, <Size n>, <Boolean for replacement> ]<br />
:Returns list of ''n'' randomly chosen elements of ''L''. Elements can be chosen several times if and only if the last parameter is true.<br />
:{{example|1=<div><code><nowiki>Sample[{1, 2, 3, 4, 5}, 5, true]</nowiki></code> yields for example ''{2, 3, 3, 4, 5}''.</div>}}<br />
==CAS Syntax==<br />
;Sample[ <List L>, <Size n> ]<br />
:Returns list of ''n'' randomly chosen elements of ''L''; elements can be chosen several times.<br />
:{{example|1=<div><code><nowiki>Sample[{-5, 2, a, 7, c}, 3]</nowiki></code> yields for example ''{a, 7, -5}''.</div>}}<br />
;Sample[ <List L>, <Size n>, <Boolean for replacement> ]<br />
:Returns list of ''n'' randomly chosen elements of ''L''. Elements can be chosen several times if and only if the last parameter is true.<br />
:{{example|1=<div>The list can include lists as well: Let ''List1'' be ''{1, 2, 3}''.<br /><code><nowiki>Sample[{List1, 4, 5, 6, 7, 8}, 3, false]</nowiki></code> yields for example ''{6, {1, 2, 3}, 4}''.</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=SDY_%E6%8C%87%E4%BB%A4&diff=4449SDY 指令2011-10-20T01:33:17Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|SDY}}<br />
;SDY[ <List of Points> ]<br />
:{{translate|SDY Command}}<br />
;SDY[ <List of Points> ]<br />
:Returns [[w:Standard_deviation|standard deviation]] of y-coordinates of [[Points and Vectors|points]] from the given [[Lists|list]].</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=SDX_%E6%8C%87%E4%BB%A4&diff=4448SDX 指令2011-10-20T01:33:02Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|SDX}}<br />
;SDX[ <List of Points> ]<br />
:{{translate|SDX Command}}<br />
;SDX[ <List of Points> ]<br />
:Returns [[w:Standard_deviation|standard deviation]] of x-coordinates of [[Points and Vectors|points]] from the given [[Lists|list]].</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=SD_%E6%8C%87%E4%BB%A4&diff=4447SD 指令2011-10-20T01:32:46Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|statistics|SD}}<br />
;SD[ <List of Numbers> ]<br />
:{{translate|SD Command}}<br />
==CAS 視窗==<br />
<br />
;SD[ <List of Numbers> ]<br />
:{{translate|SD Command}}<br />
;SD[ <List of Numbers> ]<br />
:Calculates the standard deviation of the numbers in the list.<br />
:{{example|1=<div><code><nowiki>SD[{1, 2, 3, 4, 5}]</nowiki></code> yields ''1,41''.</div>}}<br />
==CAS Syntax==<br />
;SD[ <List of Numbers> ]<br />
:Calculates the standard deviation of the numbers in the list.<br />
:{{example|1=<div><code><nowiki>SD[{1, 2, 3, 4, 5}]</nowiki></code> yields <math>\sqrt{2}</math>.</div>}}<br />
{{note| 1=<div>See also [[Mean Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Row_%E6%8C%87%E4%BB%A4&diff=4446Row 指令2011-10-20T01:32:27Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|spreadsheet|Row}}<br />
;Row[ <Spreadsheet Cell> ]<br />
:{{translate|Row Command}}<br />
; Row[Spreadsheet Cell]: Returns the row number of a spreadsheet cell (starting at 1).<br />
: {{Example| 1=<code>Row[B3]</code> gives you number ''a = 3''.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RotateText_%E6%8C%87%E4%BB%A4&diff=4445RotateText 指令2011-10-20T01:32:11Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|text|RotateText}}<br />
;RotateText[ <Text>, <Angle> ]<br />
:{{translate|RotateText Command}}<br />
;RotateText[ <Text>, <Angle> ]<br />
:Returns text rotated by given angle. [[LaTeX]] is used for rendering of the result.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Rotate_%E6%8C%87%E4%BB%A4&diff=4444Rotate 指令2011-10-20T01:30:13Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|transformation|Rotate}}<br />
;Rotate[ <Object>, <Angle> ]<br />
:{{translate|Rotate Command}}<br />
;Rotate[ <Object>, <Angle>, <Point> ]<br />
:{{translate|Rotate Command}}<br />
; Rotate[ [[Geometric Objects|Geometric Object]], Angle]: Rotates the geometric object by the angle around the axis origin. <br />
; Rotate[ Image, Angle]: Rotates the image by the angle around the axis origin. <br />
; Rotate[ [[Geometric Objects|Geometric Object]], Angle, Point P]: Rotates the geometric object by the angle around point B. <br />
; Rotate[ Image, Angle, Point P]: Rotates the image by the angle around point P. <br />
<br />
{{note|<br />
* Vectors are not rotated around axis origin or point P, but around their initial point.<br />
* When a polygon, segment or arc are rotated, also images of the vertices / endpoints and sides (in case of polygon) are created.<br />
* For text rotation use [[RotateText Command]].<br />
* See also [[Image:Tool_Rotate_Object_around_Point_by_Angle.gif ]] [[Rotate Object around Point by Angle Tool|Rotate Object around Point by Angle]] tool}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Roots_%E6%8C%87%E4%BB%A4&diff=4443Roots 指令2011-10-20T01:29:57Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|function|Roots}}<br />
;Roots[ <Function>, <Start x-Value>, <End x-Value> ]<br />
:{{translate|Roots Command}}<br />
;Roots[ <Function>, <Start x-Value>, <End x-Value> ]<br />
:Calculates the roots for function in the given interval. The function must be continuous on that interval. Because this algorithm is numeric, it may not find all the roots in some cases.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RootMeanSquare_%E6%8C%87%E4%BB%A4&diff=4442RootMeanSquare 指令2011-10-20T01:29:40Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|RootMeanSquare}}<br />
;RootMeanSquare[ <List of Numbers> ]<br />
:{{translate|RootMeanSquare Command}}<br />
;RootMeanSquare[ <List of Numbers> ]<br />
:Returns the [[w:Root mean square|root mean square]] of given list of numbers.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RootList_%E6%8C%87%E4%BB%A4&diff=4441RootList 指令2011-10-20T01:29:26Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|list|RootList}}<br />
;RootList[ <List> ]<br />
:{{translate|RootList Command}}<br />
;RootList[ <List> ]<br />
:Given a list of numbers {a<sub>1</sub>,a<sub>2</sub>,...,a<sub>n</sub>} creates list of points {(a<sub>1</sub>,0),(a<sub>2</sub>,0),...,(a<sub>n</sub>,0)}.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Root_%E6%8C%87%E4%BB%A4&diff=4440Root 指令2011-10-20T01:29:10Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|function|Root}}<br />
;Root[ <Polynomial> ]<br />
:{{translate|Root Command}}<br />
;Root[ <Function>, <Initial x-Value> ]<br />
:{{translate|Root Command}}<br />
;Root[ <Function>, <Start x-Value>, <End x-Value> ]<br />
:{{translate|Root Command}}<br />
; Root[ <Polynomial> ]<br />
:Yields all roots of the polynomial as intersection points of the function graph and the ''x''‐axis.<br />
;Root[ <Function>, <Number a> ]<br />
:Yields one root of the function using the initial value ''a'' for Newton's method.<br />
;Root[ <Function>, <Number a>, <Number b> ]<br />
:Yields one root of the function in the interval [''a, b''] (regula falsi).<br />
==CAS Syntax==<br />
;Root[ <Polynomial> ]<br />
:Yields all roots of the polynomial as intersection points of the function graph and the ''x''‐axis.<br />
:{{example| 1=<div><code><nowiki>Root[x^3 - 3 * x^2 - 4 * x + 12]</nowiki></code> yields ''{x = 3, x = 2, x = -2}''.</div>}}<br />
{{note| 1=<div>This command is only a special variant of [[Solve Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RigidPolygon_%E6%8C%87%E4%BB%A4&diff=4439RigidPolygon 指令2011-10-20T01:28:55Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry|RigidPolygon}}<br />
;RigidPolygon[ <Free Point>, ..., <Free Point> ]<br />
:{{translate|RigidPolygon Command}}<br />
;RigidPolygon[ <Free Point>, ..., <Free Point> ]<br />
:Creates polygon whose shape cannot be changed. This polygon can be translated by dragging its first vertex and rotated by dragging its second vertex.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RightSide_%E6%8C%87%E4%BB%A4&diff=4438RightSide 指令2011-10-20T01:28:25Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|CAS|RightSide}}<br />
;RightSide[ <Equation> ]<br />
:{{translate|RightSide Command}}<br />
;RightSide[ { <Equation> } ]<br />
:{{translate|RightSide Command}}<br />
;RightSide[ <Equation> ]<br />
:Returns the right-hand side of the equation.<br />
:{{example|1=<div><code><nowiki>RightSide[x + 2 = 3x + 1]</nowiki></code> yields ''3x + 1''.</div>}}<br />
;RightSide[ { <Equation> } ]<br />
:Returns the right-hand sides of the equations.<br />
:{{example|1=<div><code><nowiki>RightSide[{a^2 + b^2 = c^2, x + 2 = 3x + 1}]</nowiki></code> yields ''{c<sup>2</sup>, 3x + 1}''.</div>}}<br />
{{note| 1=<div>See also [[LeftSide Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Reverse_%E6%8C%87%E4%BB%A4&diff=4437Reverse 指令2011-10-20T01:28:10Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|list|Reverse}}<br />
;Reverse[ <List> ]<br />
:{{translate|Reverse Command}}<br />
; Reverse[List]: Reverses the order of a list.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=ResidualPlot_%E6%8C%87%E4%BB%A4&diff=4436ResidualPlot 指令2011-10-20T01:27:53Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|chart|ResidualPlot}}<br />
;ResidualPlot[ <List of Points>, <Function> ]<br />
:{{translate|ResidualPlot Command}}<br />
;ResidualPlot[ <List of Points L>, <Function f> ]<br />
:Returns a list of points whose x-coordinates are equal to x-coordinates of elements of L and y-coordinates are residuals with respect to ''f''. If ''i''-th element of L is a point ''(a,b)'' then ''i''-th element of result is ''(a,b-f(a))''.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Rename_%E6%8C%87%E4%BB%A4&diff=4435Rename 指令2011-10-20T01:27:35Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|scripting|Rename}}<br />
;Rename[ <Object>, <Name> ]<br />
:{{translate|Rename Command}}<br />
;Rename[ <Object>, <Name N> ]<br />
:Sets the [[Labels and Captions|label]] of given object to N.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RemoveUndefined_%E6%8C%87%E4%BB%A4&diff=4434RemoveUndefined 指令2011-10-20T01:27:16Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|list|RemoveUndefined}}<br />
;RemoveUndefined[ <List> ]<br />
:{{translate|RemoveUndefined Command}}<br />
; RemoveUndefined[List]: Removes undefined objects from a list. <br />
: {{Example| 1=<code>RemoveUndefined[Sequence[(-1)^i, i, -3, -1, 0.5]]</code> removes the second and fourth elements of the sequence since expressions <math>(-1)^{1.5}</math> and <math>(-1)^{2.5}</math> are undefined.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Relation_%E6%8C%87%E4%BB%A4&diff=4433Relation 指令2011-10-20T01:27:03Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|logical|Relation}}<br />
;Relation[ <Object>, <Object> ]<br />
:{{translate|Relation Command}}<br />
; Relation[Object a, Object b]: Shows a message box that gives you information about the relation between object ''a'' and object ''b''.<br />
<br />
This command allows you to find out whether<br />
* two lines are perpendicular<br />
* two lines are parallel<br />
* two objects are equal<br />
* a point lies on a line or conic<br />
* a line is tangent or a passing line to a conic.<br />
<br />
{{Note| See also [[Relation Tool|Relation]] tool. }}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Reflect_%E6%8C%87%E4%BB%A4&diff=4432Reflect 指令2011-10-20T01:26:41Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|transformation|Reflect}}<br />
;Reflect[ <Object>, <Point> ]<br />
:{{translate|Reflect Command}}<br />
;Reflect[ <Object>, <Line> ]<br />
:{{translate|Reflect Command}}<br />
;Reflect[ <Object>, <Circle> ]<br />
:{{translate|Reflect Command}}<br />
; Reflect[ [[Geometric Objects|Geometric Object]], Point B]: Reflects the geometric object through point ''B''. <br />
<br />
: {{Note| When reflecting polygons through a point, the transformed vertices and segments are created as well.}} <br />
<br />
; Reflect[Image, Point]: Reflects the image through the given point.<br />
<br />
; Reflect[ [[Geometric Objects|Geometric Object]], Line]: Reflects the geometric object across the given line.<br />
: {{Note| When reflecting polygons across a line, the transformed vertices and segments are created as well.}} <br />
<br />
; Reflect[Image, Line]: Reflects the image across the line. <br />
; Reflect[ [[Geometric Objects|Geometric Object]], Circle]: Inverts the geometric object with respect to a circle. <br />
<br />
{{Note| See also [[Reflect Object about Point Tool|Reflect Object about Point]], [[Reflect Object about Line Tool|Reflect Object about Line]] , and [[Reflect Object about Circle Tool|Reflect Object about Circle]] tools.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=ReducedRowEchelonForm_%E6%8C%87%E4%BB%A4&diff=4431ReducedRowEchelonForm 指令2011-10-20T01:26:24Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|vector-matrix|ReducedRowEchelonForm}}<br />
;ReducedRowEchelonForm[ <Matrix> ]<br />
:{{translate|ReducedRowEchelonForm Command}}<br />
==CAS 視窗==<br />
<br />
;ReducedRowEchelonForm[ <Matrix> ]<br />
:{{translate|ReducedRowEchelonForm Command}}<br />
;ReducedRowEchelonForm[ <Matrix> ]<br />
:Returns the [[w:Row_echelon_form|reduced echelon form]] of the matrix.<br />
==CAS Syntax==<br />
;ReducedRowEchelonForm[ <Matrix> ]<br />
:Returns the reduced echelon form of the matrix.<br />
:{{example| 1=<div><code><nowiki>ReducedRowEchelonForm[{{1, 6, 4}, {2, 8, 9}, {4, 5, 6}}]</nowiki></code> yields the matrix <math> \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}</math>.</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RectangleSum_%E6%8C%87%E4%BB%A4&diff=4430RectangleSum 指令2011-10-20T01:26:04Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|function|RectangleSum}}<br />
;RectangleSum[ <Function>, <Start x-Value>, <End x-Value>, <Number of Rectangles>, <Position for rectangle start> ]<br />
:{{translate|RectangleSum Command}}<br />
;RectangleSum[ <Function>, <Start x-Value>, <End x-Value>, <Number of Rectangles>, <Position for rectangle start> ]<br />
:Calculates the sum of rectangles with left height starting at a fraction d of each interval using n rectangles. (''0<=d<=1'')<br />
{{Note|* This command draws the rectangles of the left sum as well. <br />
* See also [[LeftSum Command]], [[LowerSum Command]] and [[UpperSum Command]].}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Real_%E6%8C%87%E4%BB%A4&diff=4429Real 指令2011-10-20T01:25:50Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|CAS|Real}}<br />
;Real[ <Complex Number> ]<br />
:{{translate|Real Command}}<br />
;Real[ <Complex Number>]<br />
:Returns the real part of a given [[Complex Numbers|complex number]].<br />
:{{example| 1=<div><code><nowiki>Real[17 + 3 ί]</nowiki></code> yields ''17'', the real part of the complex number ''17 + 3 ί''.</div>}}<br />
{{note| 1=<div><br />
* The complex ί is obtained by pressing {{KeyCode|ALT + i}}. <br />
* See also [[Imaginary Command]].<br />
</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Ray_%E6%8C%87%E4%BB%A4&diff=4428Ray 指令2011-10-20T01:25:35Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry|Ray}}<br />
;Ray[ <Start Point>, <Point> ]<br />
:{{translate|Ray Command}}<br />
;Ray[ <Start Point>, <Direction Vector> ]<br />
:{{translate|Ray Command}}<br />
; Ray[Point A, Point B]: Creates a ray starting at point ''A'' through point ''B''. <br />
; Ray[Point, Vector v]: Creates a ray starting at the given point which has the direction vector ''v''. <br />
<br />
{{Note| See also [[Image:Tool Ray through Two Points.gif]] [[Ray through Two Points Tool|Ray through Two Points]] tool.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Rationalize_%E6%8C%87%E4%BB%A4&diff=4427Rationalize 指令2011-10-20T01:25:21Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|CAS|Rationalize}}<br />
;Rationalize[ <Number> ]<br />
:{{translate|Rationalize Command}}<br />
;Rationalize[ <Number> ]<br />
:Creates the fraction of the given ''Number''.<br />
:{{example| 1=<div><code><nowiki>Rationalize[3.5]</nowiki></code> yields <math>\frac{7}{2}</math>.</div>}}<br />
{{note| 1=<div>See also [[MixedNumber Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomUniform_%E6%8C%87%E4%BB%A4&diff=4426RandomUniform 指令2011-10-20T01:24:47Z<p>Jackhu:en</p>
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<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|probability|RandomUniform}}<br />
;RandomUniform[ <Min>, <Max> ]<br />
:{{translate|RandomUniform Command}}<br />
;RandomUniform[ <Min>, <Max> ]<br />
:Returns random real number from [[w:Uniform distribution (continuous)|uniform distribution]] on interval [min,max].<br />
{{Note|1=<code>RandomUniform[0,1]</code> is equivalent to <code>random()</code> (see [[Predefined Functions and Operators]]).}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomPolynomial_%E6%8C%87%E4%BB%A4&diff=4425RandomPolynomial 指令2011-10-20T01:24:30Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|CAS|RandomPolynomial}}<br />
;RandomPolynomial[ <Degree> , <Minimum for Coefficients>, <Maximum for Coefficients> ]<br />
:{{translate|RandomPolynomial Command}}<br />
;RandomPolynomial[ <Variable>, <Degree> , <Minimum for Coefficients>, <Maximum for Coefficients> ]<br />
:{{translate|RandomPolynomial Command}}<br />
;RandomPolynomial[ <Degree d> , <Minimum for Coefficients min>, <Maximum for Coefficients max> ]<br />
:Returns a randomly generated polynomial in ''x'' of degree ''d'', whose (integer) coefficients are in the range from ''min'' to ''max'', both included. <br />
:{{example| 1=<div><br />
:* <code><nowiki>RandomPolynomial[0, 1, 2]</nowiki></code> yields either ''1'' or ''2'' and<br />
:* <code><nowiki>RandomPolynomial[2, 1, 2]</nowiki></code> yields a random polynomial with a degree of two and only ''1'' and ''2'' as coefficients, for example ''2x<sup>2</sup> + x + 1''.</div>}}<br />
;RandomPolynomial[ <Variable Var>, <Degree d> , <Minimum for Coefficients min>, <Maximum for Coefficients max> ]<br />
:Returns a randomly generated polynomial in ''Var'' of degree ''d'', whose (integer) coefficients are in the range from ''min'' to ''max'', both included.<br />
:{{example| 1=<div><br />
:* <code><nowiki>RandomPolynomial[a, 0, 1, 2]</nowiki></code> yields either ''1'' or ''2'' and<br />
:* <code><nowiki>RandomPolynomial[a, 2, 1, 2]</nowiki></code> yields a random polynomial with a degree of two and only ''1'' and ''2'' as coefficients, for example ''2a<sup>2</sup> + a + 1''.</div>}}<br />
{{note|In both cases if ''min'' or ''max'' are not integers, ''round(min)'' and ''round(max)'' are used instead.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomPoisson_%E6%8C%87%E4%BB%A4&diff=4424RandomPoisson 指令2011-10-20T01:24:15Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|probability|RandomPoisson}}<br />
;RandomPoisson[ <Mean> ]<br />
:{{translate|RandomPoisson Command}}<br />
==CAS 視窗==<br />
<br />
;RandomPoisson[ <Mean> ]<br />
:{{translate|RandomPoisson Command}}<br />
;RandomPoisson[ <Mean> ]<br />
:Generates a random number from a Poisson distribution with given mean.<br />
:{{example| 1=<div><code><nowiki>RandomPoisson[3]</nowiki></code> yields a random value from a Poisson distribution with a mean of ''3''.</div>}}<br />
{{note| 1=<div>See also [[RandomBinomial Command]] and [[RandomNormal Command]].</div>}}<br />
==CAS Syntax==<br />
;RandomPoisson[ <Mean> ]<br />
:Generates a random number from a Poisson distribution with given mean.<br />
:{{example| 1=<div><code><nowiki>RandomPoisson[3]</nowiki></code> yields a random value from a Poisson distribution with a mean of ''3''.</div>}}<br />
{{note| 1=<div>See also [[RandomBinomial Command]] and [[RandomNormal Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomNormal_%E6%8C%87%E4%BB%A4&diff=4423RandomNormal 指令2011-10-20T01:23:57Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|probability|RandomNormal}}<br />
;RandomNormal[ <Mean>, <Standard Deviation> ]<br />
:{{translate|RandomNormal Command}}<br />
;RandomNormal[ <Mean>, <Standard Deviation> ]<br />
:Generates a random number from a normal distribution with mean and standard deviation.<br />
:{{example| 1=<div><code><nowiki>RandomNormal[3, 0.1]</nowiki></code> yields a random value from a normal distribution with a mean of ''3'' and standard deviation of ''0.1''.</div>}}<br />
{{note| 1=<div>See also [[RandomBinomial Command]] and [[RandomPoisson Command]].</div>}}<br />
==CAS Syntax==<br />
;RandomNormal[ <Mean>, <Standard Deviation> ]<br />
:Generates a random number from a normal distribution with mean and standard deviation.<br />
:{{example| 1=<div><code><nowiki>RandomNormal[3, 0.1]</nowiki></code> yields a random value from a normal distribution with a mean of ''3'' and standard deviation of ''0.1''.</div>}}<br />
{{note| 1=<div>See also [[RandomBinomial Command]] and [[RandomPoisson Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomElement_%E6%8C%87%E4%BB%A4&diff=4422RandomElement 指令2011-10-20T01:23:38Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|list|RandomElement}}<br />
;RandomElement[ <List> ]<br />
:{{translate|RandomElement Command}}<br />
==CAS 視窗==<br />
<br />
;RandomElement[ <List> ]<br />
:{{translate|RandomElement Command}}<br />
;RandomElement[ <List> ]<br />
:Returns randomly chosen element from the [[Lists|list]] (with uniform probability). All elements in the list must be of the same type.<br />
:{{example| 1=<div><code><nowiki>RandomElement[{3, 2, -4, 7}]</nowiki></code> yields one of ''{-4, 2, 3, 7}''.</div>}}<br />
{{note| 1=<div>See also [[Element Command]].</div>}}<br />
<br />
==CAS Syntax==<br />
;RandomElement[ <List> ]<br />
:Returns randomly chosen element from the [[Lists|list]] (with uniform probability). All elements in the list must be of the same type.<br />
:{{example| 1=<div><code><nowiki>RandomElement[{3, 2, -4, 7}]</nowiki></code> yields one of ''{-4, 2, 3, 7}''.</div>}}<br />
{{note| 1=<div>See also [[Element Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomBinomial_%E6%8C%87%E4%BB%A4&diff=4421RandomBinomial 指令2011-10-20T01:23:14Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|probability|RandomBinomial}}<br />
;RandomBinomial[ <Number of Trials>, <Probability> ]<br />
:{{translate|RandomBinomial Command}}<br />
==CAS 視窗==<br />
<br />
;RandomBinomial[ <Number of Trials>, <Probability> ]<br />
:{{translate|RandomBinomial Command}}<br />
;RandomBinomial[ <Number n of Trials>, <Probability p> ]<br />
:Generates a random number from a binomial distribution with ''n'' trials and probability ''p''.<br />
:{{example| 1=<div><code><nowiki>RandomBinomial[3, 0.1]</nowiki></code> gives ''j ∈ {0, 1, 2, 3}'', where the probability of getting ''j'' is the probability of an event with probability ''0.1'' occuring ''j'' times in three tries.</div>}}<br />
==CAS Syntax==<br />
;RandomBinomial[ <Number n of Trials>, <Probability p> ]<br />
:Generates a random number from a binomial distribution with ''n'' trials and probability ''p''.<br />
:{{example| 1=<div><code><nowiki>RandomBinomial[3, 0.1]</nowiki></code> gives ''j ∈ {0, 1, 2, 3}'', where the probability of getting ''j'' is the probability of an event with probability ''0.1'' occuring ''j'' times in three tries.</div>}}<br />
{{note| 1=<div>See also [[RandomNormal Command]] and [[RandomPoisson Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RandomBetween_%E6%8C%87%E4%BB%A4&diff=4420RandomBetween 指令2011-10-20T01:22:57Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|probability|RandomBetween}}<br />
;RandomBetween[ <Minimum Integer>, <Maximum Integer> ]<br />
:{{translate|RandomBetween Command}}<br />
; RandomBetween[Min Integer, Max Integer]: Generates a random integer between ''min'' and ''max'' (inclusive).</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=RSquare_%E6%8C%87%E4%BB%A4&diff=4419RSquare 指令2011-10-20T01:22:42Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|RSquare}}<br />
;RSquare[ <List of Points>, <Function> ]<br />
:{{translate|RSquare Command}}<br />
;RSquare[ <List of Points>,<Function> ]<br />
:Calculates the [[w:Coefficient of determination|coefficient of determination]] R² = 1-SSE/Syy, between the y-values of the points in the list and the function values of the x-values in the list.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Radius_%E6%8C%87%E4%BB%A4&diff=4418Radius 指令2011-10-20T01:22:27Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry|Radius}}<br />
;Radius[ <Conic> ]<br />
:{{translate|Radius Command}}<br />
; Radius[Circle]: Returns the radius of the circle.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Q3_%E6%8C%87%E4%BB%A4&diff=4417Q3 指令2011-10-20T01:22:07Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|Q3}}<br />
;Q3[ <List of Numbers> ]<br />
:{{translate|Q3 Command}}<br />
; Q3[List of Numbers]: Determines the upper quartile of the list elements.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Q1_%E6%8C%87%E4%BB%A4&diff=4416Q1 指令2011-10-20T01:21:41Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|statistics|Q1}}<br />
;Q1[ <List of Numbers> ]<br />
:{{translate|Q1 Command}}<br />
; Q1[List of Numbers]: Determines the lower quartile of the list elements.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Product_%E6%8C%87%E4%BB%A4&diff=4415Product 指令2011-10-20T01:21:02Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|list|Product}}<br />
;Product[ <List of Numbers> ]<br />
:{{translate|Product Command}}<br />
;Product[ <List of Numbers>, <Number of Elements> ]<br />
:{{translate|Product Command}}<br />
==CAS 視窗==<br />
<br />
;Product[ <List of Numbers> ]<br />
:{{translate|Product Command}}<br />
;Product[ <List of Numbers>, <Number of Elements> ]<br />
:{{translate|Product Command}}<br />
;Product[ <List of Numbers> ]<br />
:Calculates the product of all numbers in the list.<br />
;Product[ <List of Numbers>, <Number of Elements>]<br />
:Calculates the product of the first ''n'' list elements. <br />
{{example|1=<div><code><nowiki>Product[{1, 2, 3, 4}, 3]</nowiki></code> yields ''6''.</div>}}<br />
==CAS Specific Syntax==<br />
In [[CAS View]] only the following syntax is allowed:<br />
;Product[ <List of expressions> ]:<br />
:Calculates the product of all elements in the list.<br />
:{{example|1=<div><code><nowiki>Product[{1, 2, x}]</nowiki></code> yields ''2x''.</div>}}<br />
;Product[ <Expression>, <Variable>, <Start>, <End> ]<br />
:Calculates the product of the expressions that are obtained by replacing the given variable with every integer from ''start'' to ''end''.<br />
:{{example|1=<div><code><nowiki>Product[x + 1, x, 2, 3]</nowiki></code> yields ''12''.</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PrimeFactors_%E6%8C%87%E4%BB%A4&diff=4414PrimeFactors 指令2011-10-20T01:20:44Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|algebra|PrimeFactors}}<br />
;PrimeFactors[ <Number> ]<br />
:{{translate|PrimeFactors Command}}<br />
==CAS 視窗==<br />
<br />
;PrimeFactors[ <Number> ]<br />
:{{translate|PrimeFactors Command}}<br />
;PrimeFactors[ <Number> ]<br />
:Returns the list of [[w:Prime number|primes]] whose product equals to the given number. <br />
:{{example|1=<div><br />
:* <code><nowiki>PrimeFactors[1024]</nowiki></code> yields ''{2, 2, 2, 2, 2, 2, 2, 2, 2, 2}''.<br />
:* <code><nowiki>PrimeFactors[42]</nowiki></code> yields ''{2, 3, 7}''.</div>}}<br />
{{note|See also [[Factors Command]].}}<br />
==CAS Syntax==<br />
;PrimeFactors[ <Number> ]<br />
:Returns the list of [[w:Prime number|primes]] whose product equals to the given number.<br />
:{{example|1=<div><br />
:* <code><nowiki>PrimeFactors[1024]</nowiki></code> yields ''{2, 2, 2, 2, 2, 2, 2, 2, 2, 2}''.<br />
:* <code><nowiki>PrimeFactors[42]</nowiki></code> yields ''{2, 3, 7}''.</div>}}<br />
{{note|See also [[Factors Command]].}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PreviousPrime_%E6%8C%87%E4%BB%A4&diff=4413PreviousPrime 指令2011-10-20T01:20:27Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|CAS|PreviousPrime}}<br />
;PreviousPrime[ <Number> ]<br />
:{{translate|PreviousPrime Command}}<br />
;PreviousPrime[ <Number> ]<br />
:Returns the greatest prime smaller than the entered number.<br />
:{{example| 1=<div><code><nowiki>PreviousPrime[10000]</nowiki></code> yields ''9973''.</div>}}<br />
{{note| 1=<div>See also [[NextPrime Command]].</div>}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Polynomial_%E6%8C%87%E4%BB%A4&diff=4412Polynomial 指令2011-10-20T01:20:11Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|function|Polynomial}}<br />
;Polynomial[ <Function> ]<br />
:{{translate|Polynomial Command}}<br />
;Polynomial[ <List of Points> ]<br />
:{{translate|Polynomial Command}}<br />
; Polynomial[Function]: Yields the expanded polynomial function. <br />
: {{Example|1=<code>Polynomial[(x - 3)^2]</code> yields ''x<sup>2</sup> - 6x + 9''. }}<br />
; Polynomial[List of n points]: Creates the interpolation polynomial of degree ''n-1'' through the given ''n'' points.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Polygon_%E6%8C%87%E4%BB%A4&diff=4411Polygon 指令2011-10-20T01:19:55Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry|Polygon}}<br />
;Polygon[ <Point>, ..., <Point> ]<br />
:{{translate|Polygon Command}}<br />
;Polygon[ <Point>, <Point>, <Number of Vertices> ]<br />
:{{translate|Polygon Command}}<br />
;Polygon[ <List of Points> ]<br />
:{{translate|Polygon Command}}<br />
; Polygon[Point A, Point B, Point C,...]: Returns a polygon defined by the given points ''A'', ''B'', ''C'',… <br />
; Polygon[Point A, Point B, Number n]: Creates a regular polygon with ''n'' vertices (and one side between points ''A'' and ''B'').<br />
; Polygon[List of points]: Returns a polygon defined by the points in the list. <br />
<br />
{{Note| See also [[Image:Tool Polygon.gif]] [[Polygon Tool|Polygon]] and [[Image:Tool Regular_Polygon.gif]] [[Regular Polygon Tool|Regular Polygon]] tools.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PolyLine_%E6%8C%87%E4%BB%A4&diff=4410PolyLine 指令2011-10-20T01:17:19Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry|PolyLine}}<br />
;PolyLine[ <Point>, ..., <Point> ]<br />
:{{translate|PolyLine Command}}<br />
;PolyLine[ <List of Points> ]<br />
:{{translate|PolyLine Command}}<br />
;PolyLine[ <Point>, ..., <Point> ]<br />
:Creates an open polygonal chain (i.e. a connected series of segments) having the initial vertex in the first entered point, and the final vertex in the last entered point. <br />
:{{Note|The polygonal chain length is displayed in the [[Algebra View]].}}<br />
<br />
;PolyLine[ <List of Points> ]<br />
:Creates an open polygonal chain (i.e. a connected series of segments) having the initial vertex in the first point of the list, and the final vertex in the last point of the list. <br />
:{{Note|The polygonal chain length is displayed in the [[Algebra View]].}}<br />
<br />
See also [[Polygon Command|Polygon]] command.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Polar_%E6%8C%87%E4%BB%A4&diff=4409Polar 指令2011-10-20T01:16:38Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|conic|Polar}}<br />
;Polar[ <Point>, <Conic> ]<br />
:{{translate|Polar Command}}<br />
; Polar[Point, Conic]: Creates the polar line of the given point relative to the conic section. <br />
<br />
{{Note| See also [[Image:Tool Polar_or_Diameter_Line.gif]] [[Polar or Diameter Line Tool|Polar or Diameter Line]] tool.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=Poisson_%E6%8C%87%E4%BB%A4&diff=4408Poisson 指令2011-10-20T01:16:03Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|probability|Poisson}}<br />
;Poisson[ <Mean> ]<br />
:{{translate|Poisson Command}}<br />
;Poisson[ <Mean>, <Boolean Cumulative> ]<br />
:{{translate|Poisson Command}}<br />
;Poisson[ <Mean>, <Variable Value>, <Boolean Cumulative> ]<br />
:{{translate|Poisson Command}}<br />
==CAS 視窗==<br />
<br />
;Poisson[ <Mean> ]<br />
:{{translate|Poisson Command}}<br />
;Poisson[ <Mean λ> ]<br />
:Returns a bar graph of a [[w:Poisson distribution|Poisson distribution]] with given mean λ.<br />
;Poisson[ <Mean λ>, <Boolean Cumulative> ]<br />
:Returns a bar graph of a Poisson distribution when ''Cumulative = false''. <br />
:Returns a bar graph of a cumulative Poisson distribution when ''Cumulative = true''.<br />
:The first parameter is same as above.<br />
;Poisson[ <Mean λ>, <Variable Value v>, <Boolean Cumulative> ]<br />
:Let X be a Poisson random variable.<br />
:Returns P( X = ''v'') when ''Cumulative'' = false. <br />
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.<br />
:First parameter is same as above.<br />
==CAS Specific Syntax==<br />
In [[CAS View]] only one syntax is supported:<br />
;Poisson[ <Mean λ>, <Variable Value v>, <Boolean Cumulative> ]<br />
:Let X be a Poisson random variable.<br />
:Returns P( X = ''v'') when ''Cumulative'' = false. <br />
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.<br />
:First parameter is same as above.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PointList_%E6%8C%87%E4%BB%A4&diff=4407PointList 指令2011-10-20T01:15:46Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|list|PointList}}<br />
;PointList[ <List> ]<br />
:{{translate|PointList Command}}<br />
;PointList[ <List> ]<br />
:Creates list of points from a list of two-element lists.<br />
{{example|1=<code>PointList[{{1,2},{3,4}}]</code> returns {(1,2),(3,4)}.}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PointIn_%E6%8C%87%E4%BB%A4&diff=4406PointIn 指令2011-10-20T01:15:25Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry|PointIn}}<br />
;PointIn[ <Region> ]<br />
:{{translate|PointIn Command}}<br />
;PointIn[ <Region> ]<br />
:Returns a point restricted to given [[Geometric Objects#Regions|region]].<br />
<br />
{{Note|See also [[Image:Tool_Attach_Detach_Point.gif]] [[Attach / Detach Point Tool]].}}</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PlaySound_%E6%8C%87%E4%BB%A4&diff=4405PlaySound 指令2011-10-20T01:15:09Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|scripting|PlaySound}}<br />
;PlaySound[ <Note>, <Duration>, <Instrument> ]<br />
:{{translate|PlaySound Command}}<br />
;PlaySound[ <Note Sequence>, <Instrument> ]<br />
:{{translate|PlaySound Command}}<br />
;PlaySound[ <File> ]<br />
:{{translate|PlaySound Command}}<br />
;PlaySound[ <Function>, <Min Value>, <Max Value> ]<br />
:{{translate|PlaySound Command}}<br />
;PlaySound[ <Function>, <Min Value>, <Max Value>, <Sample Rate>, <Sample Depth><br />
:{{translate|PlaySound Command}}<br />
;PlaySound[ <Boolean Play> ] ]<br />
:{{translate|PlaySound Command}}<br />
;PlaySound[ <Note>, <Duration>, <Instrument> ]<br />
:Plays a MIDI note. <br />
:''Note'' is an integer from 0 to 127 that represents a musical note given by the table below. When note = 60 a Middle C is played. <br />
:''Duration'' is the time to play the note in seconds. <br />
:''Instrument'' is an integer that represents the synthesized instrument used to play the note. See [http://www.midi.org/techspecs/gm1sound.php technical specifications at midi.org] for possible instruments. <br />
:Most instruments are supported, but there are differences between computer platforms.<br />
::{| class="pretty"<br />
|+ '''MIDI Notes'''<br />
!Octave<br />
!C <br />
!C# <br />
!D <br />
!D# <br />
!E <br />
!F <br />
!F# <br />
!G <br />
!G# <br />
!A <br />
!A# <br />
!B<br />
|+<br />
|'''0'''<br />
|0 <br />
|1 <br />
|2 <br />
|3 <br />
|4 <br />
|5 <br />
|6 <br />
|7 <br />
|8 <br />
|9 <br />
|10 <br />
|11<br />
|+<br />
|'''1'''<br />
|12 <br />
|13 <br />
|14 <br />
|15 <br />
|16 <br />
|17 <br />
|18 <br />
|19 <br />
|20 <br />
|21 <br />
|22 <br />
|23<br />
|+<br />
|'''2'''<br />
|24 <br />
|25 <br />
|26 <br />
|27 <br />
|28 <br />
|29 <br />
|30 <br />
|31 <br />
|32 <br />
|33 <br />
|34 <br />
|35<br />
|+<br />
|'''3''' <br />
|36 <br />
|37 <br />
|38 <br />
|39 <br />
|40 <br />
|41 <br />
|42 <br />
|43 <br />
|44 <br />
|45 <br />
|46<br />
|47<br />
|+<br />
|'''4''' <br />
|48 <br />
|49 <br />
|50 <br />
|51 <br />
|51 <br />
|53 <br />
|54 <br />
|55 <br />
|56 <br />
|57 <br />
|58<br />
|59<br />
|+<br />
|'''5''' <br />
|60 <br />
|61 <br />
|62 <br />
|63 <br />
|64 <br />
|65 <br />
|66 <br />
|67 <br />
|68 <br />
|69 <br />
|70<br />
|71<br />
|+<br />
|'''6''' <br />
|72 <br />
|73 <br />
|74 <br />
|75 <br />
|76 <br />
|77 <br />
|78 <br />
|79 <br />
|80 <br />
|81 <br />
|82<br />
|83<br />
|+<br />
|'''7''' <br />
|84 <br />
|85 <br />
|86 <br />
|87 <br />
|88 <br />
|89 <br />
|90 <br />
|91 <br />
|92 <br />
|93 <br />
|94<br />
|95<br />
|+<br />
|'''8''' <br />
|96 <br />
|97 <br />
|98 <br />
|99 <br />
|100 <br />
|101<br />
|102 <br />
|103 <br />
|104 <br />
|105 <br />
|106<br />
|107<br />
|+<br />
|'''9''' <br />
|108 <br />
|109 <br />
|110 <br />
|111 <br />
|112 <br />
|113 <br />
|114 <br />
|115 <br />
|116 <br />
|117 <br />
|118<br />
|119<br />
|+<br />
|'''10'''<br />
|120 <br />
|121 <br />
|122 <br />
|123 <br />
|124 <br />
|125 <br />
|126 <br />
|127 <br />
|<br />
|<br />
|<br />
| <br />
|+<br />
|} <br />
<br />
<br />
<br />
;PlaySound[ <Note Sequence>, <Instrument> ]<br />
: Plays a sequence of MIDI notes and commands using a [http://www.jfugue.org JFugue ] music string.<br />
: ''Note Sequence'' is a text string that uses JFugue character commands. <br />
: ''Instrument'' is the default MIDI instrument used when the string is played. <br />
: The basic commands are given below. The full command set is described in <br />
: [http://www.jfugue.org/jfugue-chapter1.pdf The Complete Guide to JFugue ] (English).<br />
<br />
<br />
::{| class="pretty"<br />
|+ '''Basic JFugue Commands'''<br />
!Character<br />
!Command<br />
<br />
|+<br />
| A-G <br />
| Play the musical note given by the letter in octave 5<br />
: For sharps and flats add b or #<br />
: To change octaves add the octave number, e.g. A4<br />
: Note length is a quarter note unless specified otherwise<br />
<br />
|+<br />
| [number] <br />
| Play the MIDI note given by the number (0-127)<br />
<br />
|+<br />
| +<br />
| Join notes together to play them in harmony, e.g. C+E+G<br />
<br />
|+<br />
| R <br />
| Rest<br />
<br />
|+<br />
| w, h, q, i, s <br />
| Add to the end of a note or rest; sets the length <br />
:: w = whole note<br />
:: h = half note<br />
:: q = quarter note<br />
:: i = eighth note<br />
:: s = sixteenth note<br />
<br />
|+<br />
| /n <br />
| Add to a note or rest; sets the length to n (a decimal number) <br />
:: /1 = whole note <br />
:: /.5 = half note <br />
:: /.25 = quarter note <br />
:: /2 = two measures<br />
<br />
|+<br />
| I[number] <br />
| Set the instrument<br />
<br />
|+<br />
| V <br />
| V followed by a number from 0 to 15 sets the MIDI channel. "V9" sets the MIDI percussion channel.<br />
|+<br />
| Space<br />
| Play the previous note, combination of notes or rest.<br />
|}<br />
<br />
<br />
{{Example| 1=<code>PlaySound["C+E+G Rw Ai Bi Ci A4i B4i C4i ", 0]</code> <br />
: Plays a quarter note chord CEG; rests for a whole note; plays the eighth notes A, B, C; plays them again one octave lower.<br />
: Piano instrument is used.<br />
}}<br />
{{Example| 1=<code>PlaySound["I[56] C5q D5q I[71] G5q F5q", 0]</code> <br />
: Plays notes with different instruments. Trumpet = 56 and Clarinet = 71.<br />
}}<br />
{{Example| 1=<code>PlaySound["V0 A3q B3q C3q B3q V1 A2h C2h", 0]</code> <br />
: Plays notes in harmony with different voices.<br />
}}<br />
<br />
;PlaySound[ <File> ]<br />
: Plays a MIDI file (*.mid) or a text file (* .txt) containing a JFugue string. <br />
: "File" is the directory path to this file, e.g. PlaySound["path/to/myFile.mid"]<br />
<br />
;PlaySound[ <Function>, <Min Value>, <Max Value> ]<br />
:Plays a sound generated by Function, a time-valued function with range [-1,1]. The time units are seconds and the sound is played from time Min Value to Max Value. Sound is generated by 8-bit samples taken at a rate of 8000 samples per second. <br />
<br />
{{Example| 1=<code>PlaySound[sin(440 2Pi x), 0, 1]</code> <br />
:This plays a pure sine wave tone at 440 Hz (musical note A) for one second.<br />
}}<br />
<br />
<br />
;PlaySound[ <Function>, <Min Value>, <Max Value>, <Sample Rate>, <Sample Depth> ]<br />
:Plays a sound generated by Function, a time-valued function with range [-1,1]. The time units are seconds and the sound is played from time Min Value to Max Value. The sampling method is specified by "Sample Depth" and "Sample Rate". <br />
:"Sample Rate" is the number of sample function values taken each second. Allowable values are 8000, 11025, 16000, 22050, or 44100 <br />
:"Sample Depth" is the data size of a sample in bits. Allowable values are 8 and 16.<br />
<br />
<br />
;PlaySound[ <Boolean Play> ] <br />
:Pause or resume play. <br />
:PlaySound[true] = play, PlaySound[false] = pause.</div>Jackhuhttps://wiki.geogebra.org/s/zh/index.php?title=PerpendicularVector_%E6%8C%87%E4%BB%A4&diff=4404PerpendicularVector 指令2011-10-20T01:10:15Z<p>Jackhu:en</p>
<hr />
<div><noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|cas=true|vector-matrix|PerpendicularVector}}<br />
;PerpendicularVector[ <Line> ]<br />
:{{translate|PerpendicularVector Command}}<br />
;PerpendicularVector[ <Segment> ]<br />
:{{translate|PerpendicularVector Command}}<br />
;PerpendicularVector[ <Vector> ]<br />
:{{translate|PerpendicularVector Command}}<br />
==CAS 視窗==<br />
<br />
;PerpendicularVector[ <Line> ]<br />
:{{translate|PerpendicularVector Command}}<br />
;PerpendicularVector[Line]<br />
:Returns the perpendicular vector of the line. <br />
:{{note|1=A line with equation ''ax + by = c'' has the perpendicular vector ''(a, b)''.}}<br />
;PerpendicularVector[Segment]<br />
:Returns the perpendicular vector of the segment with the same length. <br />
; PerpendicularVector[Vector v]<br />
:Returns the perpendicular vector of the given vector.<br />
:{{note| A vector with coordinates ''(a, b)'' has the perpendicular vector ''(-b, a)''.}}<br />
==CAS Syntax==<br />
; PerpendicularVector[Vector v]<br />
:Returns the perpendicular vector of the given vector. <br />
:{{example|1=<div><br />
:* <code><nowiki>PerpendicularVector[(3, 2)]</nowiki></code> yields the vector ''{-2, 3}''.<br />
:* <code><nowiki>PerpendicularVector[(a, b)]</nowiki></code> yields the vector ''{-b, a}''.</div>}}<br />
{{note| 1=<div>See also [[UnitPerpendicularVector Command]].</div>}}</div>Jackhu