View source for Dilate

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      <td valign="top"><apll>Z←&gt;R</apll></td>
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      <td>extracts from <apll>R</apll> its Hypercomplex coefficients.</td>
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  <td><apll>R</apll> is an arbitrary Real or Hypercomplex numeric array &mdash; otherwise, <apll>DOMAIN ERROR</apll>.</td>
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  <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>
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<br />
<p>For example,</p>

<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍴⎕←&gt;23<br />
23<br />
1<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍴⎕←&gt;2 2⍴⍳4<br />
1<br />
2<br />
<br />
3<br />
4<br />
2 2 1<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍴⎕←&gt;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 />
3 4<br />
<br />
4 3<br />
2 1<br />
2 2 2<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍴⎕←&gt;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 />
5 6 7 8<br />
<br />
8 7 6 5<br />
4 3 2 1<br />
2 2 4 <br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍴⎕←&gt;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 />
&nbsp;1&nbsp;&nbsp;2&nbsp;&nbsp;3&nbsp;&nbsp;4&nbsp;&nbsp;5&nbsp;&nbsp;6&nbsp;&nbsp;7&nbsp;&nbsp;8<br />
&nbsp;9 10 11 12 13 14 15 16<br />
<br />
16 15 14 13 12 11 10&nbsp;&nbsp;9<br />
&nbsp;8&nbsp;&nbsp;7&nbsp;&nbsp;6&nbsp;&nbsp;5&nbsp;&nbsp;4&nbsp;&nbsp;3&nbsp;&nbsp;2&nbsp;&nbsp;1<br />
2 2 8<br />
</apll>

==Identities==

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

== Acknowledgements==

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