System Function DC - Revision history

WikiSysop: /* Dyadic Function */

2023-11-09T14:49:47Z

Dyadic Function

← Older revision		Revision as of 10:49, 9 November 2023
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	\|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}		\|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}
	{{BoxLine\|<apll>R</apll> is a numeric array.}}		{{BoxLine\|<apll>R</apll> is a numeric array.}}
	{{BoxLine\|If <apll>L</apll> is a character scalar or one-element vector ~~datatype~~ (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>) ~~indicating~~ the datatype to which the coefficients of <apll>R</apll> should be converted.}}		{{BoxLine\|If <apll>L</apll> is a character scalar or one-element vector whose value is one of (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>), this value indicates the datatype to which the coefficients of <apll>R</apll> should be converted.}}
	{{BoxLine\|If <apll>L</apll> is a numeric scalar or one-element vector, then its datatype is the datatype to which the coefficients of <apll>R</apll> should be converted.}}		{{BoxLine\|If <apll>L</apll> is a numeric scalar or one-element vector, then its datatype is the datatype to which the coefficients of <apll>R</apll> should be converted.}}
	{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.		{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.

WikiSysop: /* Dyadic Function */

2023-11-05T02:24:35Z

Dyadic Function

← Older revision		Revision as of 22:24, 4 November 2023
Line 23:		Line 23:
	\|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}		\|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}
	{{BoxLine\|<apll>R</apll> is a numeric array.}}		{{BoxLine\|<apll>R</apll> is a numeric array.}}
	{{BoxLine\|<apll>L</apll> is a character scalar or one-element vector datatype (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>) indicating the datatype to which the coefficients should be converted.}}		{{BoxLine\|If <apll>L</apll> is a character scalar or one-element vector datatype (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>) indicating the datatype to which the coefficients of <apll>R</apll> should be converted.}}
			{{BoxLine\|If <apll>L</apll> is a numeric scalar or one-element vector, then its datatype is the datatype to which the coefficients of <apll>R</apll> should be converted.}}
	{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.		{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.
	The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}		The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}
Line 30:		Line 31:
	For example,		For example,

	<apll>      'R' ⎕DC 1.5<~~hc>i<~~/hc>3		<apll>      'R' ⎕DC 1.5<_i/>3
	3<~~pn>r<~~/pn>2<~~hc>i<~~/hc>3		3<_r/>2<_i/>3
	'R' ⎕DC 1.1<~~hc>i<~~/hc>3		'R' ⎕DC 1.1<_i/>3
	2476979795053773<~~pn>r<~~/pn>2251799813685248<~~hc>i<~~/hc>3		2476979795053773<_r/>2251799813685248<_i/>3
	'F' ⎕DC 3<~~pn>r<~~/pn>2 2476979795053773<~~pn>r<~~/pn>2251799813685248		'F' ⎕DC 3<_r/>2 2476979795053773<_r/>2251799813685248
	1.5 1.1</apll>		1.5 1.1
			0 ⎕DR ⎕←0<_x/> ⎕DC 2<_i/>1
			2<_i/>1
			Complex Rational (1416): arbitrary precision numerator and denominator
			</apll>
	<br/>		<br/>
	{{SFDM\|DC}}		{{SFDM\|DC}}

WikiSysop: /* Monadic Function */

2023-11-05T02:04:25Z

Monadic Function

← Older revision		Revision as of 22:04, 4 November 2023
Line 5:		Line 5:
	{{BoxLine \|<apll>R</apll> is a numeric array.}}		{{BoxLine \|<apll>R</apll> is a numeric array.}}
	{{BoxEnd \|		{{BoxEnd \|
	<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional — BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll> where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number. '''This capability has been replaced by the [[Condense]] function (<apll><R</apll>).'''</li>		<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional — BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll>, where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number. '''This capability has been replaced by the [[Condense]] function (<apll><R</apll>).'''</li>
	<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>. '''This capability has been replaced by the [[Dilate]] function (<apll>>R</apll>).'''</li></ul>}}		<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>. '''This capability has been replaced by the [[Dilate]] function (<apll>>R</apll>).'''</li></ul>}}
	<br />		<br />
Line 18:		Line 18:
	0 1		0 1
	0 ¯1</pre></apll>		0 ¯1</pre></apll>


	==Dyadic Function==		==Dyadic Function==

WikiSysop at 05:24, 16 April 2018

2018-04-16T05:24:11Z

← Older revision		Revision as of 01:24, 16 April 2018
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	<br />		<br />
	<p>For example,</p>		<p>For example,</p>
	<apll>~~      ~~⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1~~<br />~~1 ¯1 0<pn>i</pn>1 0<pn>i</pn>¯1 ~~     ~~⍝ ~~</apll>~~The four units for Complex numbers~~<br />~~		<apll><pre>
	~~<apll>      ~~⎕DC a~~<br />~~		⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1
	~~ ~~1~~ ~~ 0~~<br />~~		1 ¯1 0<hc>i</hc>1 0<hc>i</hc>¯1 ⍝ The four units for Complex numbers
	¯1~~ ~~ 0~~<br />~~		⎕DC a
	~~ ~~0~~ ~~ 1~~<br />~~		1 0
	~~ ~~0 ¯1</~~apll~~>		¯1 0
	<~~br /><br~~ />		0 1
			0 ¯1</pre></apll>


	==Dyadic Function==		==Dyadic Function==
Line 25:		Line 27:
	{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.		{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.
	The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}		The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}
	<br />~~<p>~~For example,~~</p>~~<apll>      'R' ⎕DC 1.5<pn>i</pn>3~~<br />~~3<pn>r</pn>2<pn>i</pn>3~~<br />~~      'R' ⎕DC 1.1<pn>i</pn>3~~<br />~~2476979795053773<pn>r</pn>2251799813685248<pn>i</pn>3~~<br />~~      'F' ⎕DC 3<pn>r</pn>2 2476979795053773<pn>r</pn>2251799813685248~~<br />~~1.5 1.1</apll>		<br />

			For example,

			<apll>      'R' ⎕DC 1.5<hc>i</hc>3
			3<pn>r</pn>2<hc>i</hc>3
			'R' ⎕DC 1.1<hc>i</hc>3
			2476979795053773<pn>r</pn>2251799813685248<hc>i</hc>3
			'F' ⎕DC 3<pn>r</pn>2 2476979795053773<pn>r</pn>2251799813685248
			1.5 1.1</apll>
	<br/>		<br/>
	{{SFDM\|DC}}		{{SFDM\|DC}}

WikiSysop: /* Monadic Function */

2017-04-09T22:33:09Z

Monadic Function

← Older revision		Revision as of 18:33, 9 April 2017
Line 5:		Line 5:
	{{BoxLine \|<apll>R</apll> is a numeric array.}}		{{BoxLine \|<apll>R</apll> is a numeric array.}}
	{{BoxEnd \|		{{BoxEnd \|
	<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional — BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll> where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number.</li>		<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional — BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll> where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number. '''This capability has been replaced by the [[Condense]] function (<apll><R</apll>).'''</li>
	<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>.</li></ul>}}		<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>. '''This capability has been replaced by the [[Dilate]] function (<apll>>R</apll>).'''</li></ul>}}
	<br />		<br />
	<br />		<br />

WikiSysop: /* Monadic Function */

2016-04-22T22:09:00Z

Monadic Function

← Older revision		Revision as of 18:09, 22 April 2016
Line 5:		Line 5:
	{{BoxLine \|<apll>R</apll> is a numeric array.}}		{{BoxLine \|<apll>R</apll> is a numeric array.}}
	{{BoxEnd \|		{{BoxEnd \|
	<ul><li>For ~~1-measureable <apll>R</apll> (that is,~~ simple numeric~~, e~~.g. BOOL, INT, APA, FLOAT, RAT, or VFP) where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose ~~measure~~ is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number.</li>		<ul><li>For simple numeric (a.k.a. Hypercomplex 1-dimensional — BOOL, INT, APA, FLOAT, RAT, or VFP) <apll>R</apll> where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose Hypercomplex dimension is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number.</li>
	<li>For 2-, 4-, or 8-~~measurable~~ <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new ~~dimension~~ on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>.</li></ul>}}		<li>For Hypercomplex 2-, 4-, or 8-dimensional <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new coordinate on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>.</li></ul>}}
	<br />		<br />
	<br />		<br />
	<p>For example,</p>		<p>For example,</p>
	<apll>      ⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1<br />1 ¯1 0<pn>i</pn>1 0<pn>i</pn>¯1 ~~</apll>~~     The four units for Complex numbers<br />		<apll>      ⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1<br />1 ¯1 0<pn>i</pn>1 0<pn>i</pn>¯1      ⍝ </apll>The four units for Complex numbers<br />
	<apll>      ⎕DC a<br />		<apll>      ⎕DC a<br />
	1  0<br />		1  0<br />

WikiSysop at 00:17, 22 August 2015

2015-08-22T00:17:26Z

← Older revision		Revision as of 20:17, 21 August 2015
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	\|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}		\|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}
	{{BoxLine\|<apll>R</apll> is a numeric array.}}		{{BoxLine\|<apll>R</apll> is a numeric array.}}
	{{BoxLine\|<apll>L</apll> is a character scalar or one-element vector datatype (<apll>I F R V</apll>) indicating the datatype to which the coefficients should be converted.}}		{{BoxLine\|<apll>L</apll> is a character scalar or one-element vector datatype (<apll>'I'</apll>, <apll>'F'</apll>, <apll>'R'</apll>, or <apll>'V'</apll>) indicating the datatype to which the coefficients should be converted.}}
	{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.		{{BoxEnd\|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.
	The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}		The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}
	<br /><p>For example,</p><apll>      'r' ⎕DC 1.5<pn>i</pn>3<br />3<pn>r</pn>2<pn>i</pn>3<br />      'r' ⎕DC 1.1<pn>i</pn>3<br />2476979795053773<pn>r</pn>2251799813685248<pn>i</pn>3<br />      'f' ⎕DC 3<pn>r</pn>2 2476979795053773<pn>r</pn>2251799813685248<br />1.5 1.1</apll>		<br /><p>For example,</p><apll>      'R' ⎕DC 1.5<pn>i</pn>3<br />3<pn>r</pn>2<pn>i</pn>3<br />      'R' ⎕DC 1.1<pn>i</pn>3<br />2476979795053773<pn>r</pn>2251799813685248<pn>i</pn>3<br />      'F' ⎕DC 3<pn>r</pn>2 2476979795053773<pn>r</pn>2251799813685248<br />1.5 1.1</apll>
	<br/>		<br/>
	{{SFDM\|DC}}		{{SFDM\|DC}}

WikiSysop: Created page with "This function is available in both ''monadic'' and ''dyadic'' forms. ==Monadic Function== {{BoxStart|Z←⎕DC R |converts R between the coefficients..."

2015-08-22T00:14:46Z

Created page with "This function is available in both ''monadic'' and ''dyadic'' forms. ==Monadic Function== {{BoxStart|<apll>Z←⎕DC R</apll> |converts <apll>R</apll> between the coefficients..."

New page

This function is available in both ''monadic'' and ''dyadic'' forms.
==Monadic Function==
{{BoxStart|<apll>Z←⎕DC R</apll>
|converts <apll>R</apll> between the coefficients of a Hypercomplex number and the corresponding Hypercomplex number.}}
{{BoxLine |<apll>R</apll> is a numeric array.}}
{{BoxEnd |
<ul><li>For 1-measureable <apll>R</apll> (that is, simple numeric, e.g. BOOL, INT, APA, FLOAT, RAT, or VFP) where the number of columns of <apll>R</apll> (call that <apll>NC</apll>) is <apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>, <apll>Z</apll> is the corresponding Hypercomplex array whose measure is the same as the number of columns of <apll>R</apll>, and whose shape is <apll>¯1↓⍴R</apll>. That is, the values in the last coordinate of <apll>R</apll> are treated as the coefficients of a Hypercomplex number and <apll>Z</apll> is the corresponding Hypercomplex number.</li>
<li>For 2-, 4-, or 8-measurable <apll>R</apll>, <apll>Z</apll> is the corresponding simple array (INT, FLOAT, RAT, or VFP) with a new dimension on the right consisting of the coefficients of the Hypercomplex numbers in <apll>R</apll>, and whose shape is <apll>(⍴R),NC</apll>. That is, <apll>Z</apll> contains the coefficients of the Hypercomplex number <apll>R</apll>.</li></ul>}}
 
 
For example,
<apll>      ⎕←a←⎕DC 4 2⍴1 0 ¯1 0 0 1 0 ¯1 1 ¯1 0<pn>i</pn>1 0<pn>i</pn>¯1 </apll>     The four units for Complex numbers 
<apll>      ⎕DC a 
 1  0 
¯1  0 
 0  1 
 0 ¯1</apll>
 

==Dyadic Function==
{{BoxStart|<apll>Z←L ⎕DC R</apll>
|converts the coefficients of <apll>R</apll> to the datatype indicated by <apll>L</apll>.}}
{{BoxLine|<apll>R</apll> is a numeric array.}}
{{BoxLine|<apll>L</apll> is a character scalar or one-element vector datatype (<apll>I F R V</apll>) indicating the datatype to which the coefficients should be converted.}}
{{BoxEnd|<apll>Z</apll> is <apll>R</apll> where all of the coefficients of each of the values are converted to the datatype indicated by <apll>L</apll>.
The shape of <apll>Z</apll> is the same as that of <apll>R</apll>.}}
 For example,<apll>      'r' ⎕DC 1.5<pn>i</pn>3 3<pn>r</pn>2<pn>i</pn>3       'r' ⎕DC 1.1<pn>i</pn>3 2476979795053773<pn>r</pn>2251799813685248<pn>i</pn>3       'f' ⎕DC 3<pn>r</pn>2 2476979795053773<pn>r</pn>2251799813685248 1.5 1.1</apll>
 
{{SFDM|DC}}