Dilate - Revision history

Sudleyplace at 21:13, 15 April 2018

2018-04-15T21:13:58Z

WikiSysop at 00:42, 12 April 2018

2018-04-12T00:42:57Z

← Older revision		Revision as of 20:42, 11 April 2018
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	<table border="0" cellpadding="5" cellspacing="0" summary="">		<table border="0" cellpadding="5" cellspacing="0" summary="">
	<tr>		<tr>
	<td valign="top"><apll>Z←>R</apll></td>		<td valign="top"><apll>Z←>R</apll>    or    <apll>Z←>[X] R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	</table>		</table>
	</td>		</td>
			</tr>
			<tr>
			<td><apll>X</apll> is an optional numeric singleton axis with <apll>X∊⍳1+⍴⍴R</apll>. If X is omitted, it defaults to the last axis plus one.</td>
	</tr>		</tr>
	<tr>		<tr>
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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>Z</apll> is the corresponding array of Real numbers of shape <apll>(⍴R)~~,=R~~</apll> where <apll>=R</apll> is the Hypercomplex dimension (<apll>1</apll>, <apll>2~~</apll>, <apll>~~4~~</apll>, or <apll>~~8~~</apll>) of <apll>R~~</apll>.</td>		<td><apll>Z</apll> is the corresponding array of Real numbers of shape <apll>((=R),⍴R)[⍋⍋X≠⍳1+⍴⍴R]</apll> where <apll>=R</apll> is the Hypercomplex dimension of <apll>R</apll> as in <apll>(=R)∊1 2 4 8</apll>.</td>
	</tr>		</tr>
	</table>		</table>
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	4 3<br />		4 3<br />
	2 1<br />		2 1<br />
			2 2 2<br />
			⍴⎕←>[1] 2 2⍴1<pn>J</pn>2 3<pn>J</pn>4 4<pn>J</pn>3 2<pn>J</pn>1<br />
			1 3<br />
			4 2<br />
			<br />
			2 4<br />
			3 1<br />
	2 2 2<br />		2 2 2<br />
	⍴⎕←>2 2⍴1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4 5<pn>i</pn>6<pn>j</pn>7<pn>k</pn>8 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5 4<pn>i</pn>3<pn>j</pn>2<pn>k</pn>1<br />		⍴⎕←>2 2⍴1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4 5<pn>i</pn>6<pn>j</pn>7<pn>k</pn>8 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5 4<pn>i</pn>3<pn>j</pn>2<pn>k</pn>1<br />
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	==Identities==		==Identities==

	<apll>R ←→ <>R</apll>   for all <apll>R</apll> (see [[Condense]] for the definition of monadic Left Caret)<br />		<apll>R ←→ <[X] >[X] R</apll>   for all <apll>R</apll> (see [[Condense]] for the definition of monadic Left Caret)<br />
	<apll>R ←→ ><R</apll>   for all <apll>R</apll> with <apll>(~~¯1↑⍴R~~)∊1 2 4 8</apll><br />		<apll>R ←→ >[X] <[X] R</apll>   for all <apll>R</apll> with <apll>(⍴R)[X]∊1 2 4 8</apll><br />

	== Acknowledgements==		== Acknowledgements==

	<p>This symbol and its name were suggested by David A. Rabenhorst.</p>		<p>This symbol and its name were suggested by David A. Rabenhorst.</p>

WikiSysop at 22:59, 9 April 2017

2017-04-09T22:59:31Z

← Older revision		Revision as of 18:59, 9 April 2017
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	4<br />		4<br />
	2 2 1<br />		2 2 1<br />
	⍴⎕←>2 ~~2⍴1J2 3J4 4J3 2J1~~<br />		⍴⎕←>2 2⍴1<pn>J</pn>2 3<pn>J</pn>4 4<pn>J</pn>3 2<pn>J</pn>1<br />
	1 2<br />		1 2<br />
	3 4<br />		3 4<br />
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	2 1<br />		2 1<br />
	2 2 2<br />		2 2 2<br />
	⍴⎕←>2 ~~2⍴1i2j3k4 5i6j7k8 8i7j6k5 4i3j2k1~~<br />		⍴⎕←>2 2⍴1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4 5<pn>i</pn>6<pn>j</pn>7<pn>k</pn>8 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5 4<pn>i</pn>3<pn>j</pn>2<pn>k</pn>1<br />
	1 2 3 4<br />		1 2 3 4<br />
	5 6 7 8<br />		5 6 7 8<br />
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	4 3 2 1<br />		4 3 2 1<br />
	2 2 4 <br />		2 2 4 <br />
	⍴⎕←>2 ~~2⍴1i2j3k4l5ij6jk7kl8 9i10j11k12l13ij14jk15kl16 16i15j14k13l12ij11jk10kl9 8i7j6k5l4ij3jk2kl1~~<br />		⍴⎕←>2 2⍴1<pn>i</pn>2<pn>j</pn>3<pn>k</pn>4<pn>l</pn>5<pn>ij</pn>6<pn>jk</pn>7<pn>kl</pn>8 9<pn>i</pn>10<pn>j</pn>11<pn>k</pn>12<pn>l</pn>13<pn>ij</pn>14<pn>jk</pn>15<pn>kl</pn>16 16<pn>i</pn>15<pn>j</pn>14<pn>k</pn>13<pn>l</pn>12<pn>ij</pn>11<pn>jk</pn>10<pn>kl</pn>9 8<pn>i</pn>7<pn>j</pn>6<pn>k</pn>5<pn>l</pn>4<pn>ij</pn>3<pn>jk</pn>2<pn>kl</pn>1<br />
	1  2  3  4  5  6  7  8<br />		1  2  3  4  5  6  7  8<br />
	9 10 11 12 13 14 15 16<br />		9 10 11 12 13 14 15 16<br />

WikiSysop: Created page with "

2017-04-09T20:59:48Z

Created page with "<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""> <tr> <td> <table border="0" cellpadding="5" cellspacing="0" summary=""> <tr> <td val..."

New page
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
<tr>
<td>
<table border="0" cellpadding="5" cellspacing="0" summary="">
<tr>
<td valign="top"><apll>Z←>R</apll></td>
<td></td>
<td></td>
<td>extracts from <apll>R</apll> its Hypercomplex coefficients.</td>
</tr>
</table>
</td>
</tr>
<tr>
<td><apll>R</apll> is an arbitrary Real or Hypercomplex numeric array — otherwise, <apll>DOMAIN ERROR</apll>.</td>
</tr>
<tr>
<td><apll>Z</apll> is the corresponding array of Real numbers of shape <apll>(⍴R),=R</apll> where <apll>=R</apll> is the Hypercomplex dimension (<apll>1</apll>, <apll>2</apll>, <apll>4</apll>, or <apll>8</apll>) of <apll>R</apll>.</td>
</tr>
</table>
 
For example,

<apll>      ⍴⎕←>23 
23 
1 
      ⍴⎕←>2 2⍴⍳4 
1 
2 
 
3 
4 
2 2 1 
      ⍴⎕←>2 2⍴1J2 3J4 4J3 2J1 
1 2 
3 4 
 
4 3 
2 1 
2 2 2 
      ⍴⎕←>2 2⍴1i2j3k4 5i6j7k8 8i7j6k5 4i3j2k1 
1 2 3 4 
5 6 7 8 
 
8 7 6 5 
4 3 2 1 
2 2 4 
      ⍴⎕←>2 2⍴1i2j3k4l5ij6jk7kl8 9i10j11k12l13ij14jk15kl16 16i15j14k13l12ij11jk10kl9 8i7j6k5l4ij3jk2kl1 
 1  2  3  4  5  6  7  8 
 9 10 11 12 13 14 15 16 
 
16 15 14 13 12 11 10  9 
 8  7  6  5  4  3  2  1 
2 2 8 
</apll>

==Identities==

<apll>R ←→ <>R</apll>   for all <apll>R</apll> (see [[Condense]] for the definition of monadic Left Caret) 
<apll>R ←→ ><R</apll>   for all <apll>R</apll> with <apll>(¯1↑⍴R)∊1 2 4 8</apll> 

== Acknowledgements==

This symbol and its name were suggested by David A. Rabenhorst.