Difference between revisions of "Commute-Duplicate"

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(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...")
 
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     <tr>
 
     <tr>
       <td valign="top">Commute: <apll>Z←f⍨ R</apll></td>
+
       <td valign="top">Duplicate: <apll>Z←f⍨ R</apll></td>
 
       <td></td>
 
       <td></td>
 
       <td>&nbsp;&nbsp;&nbsp;&nbsp;</td>
 
       <td>&nbsp;&nbsp;&nbsp;&nbsp;</td>
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     <tr>
 
     <tr>
       <td valign="top">Duplicate:  <apll>Z←L f⍨ R</apll></td>
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       <td valign="top">Commute:  <apll>Z←L f⍨ R</apll></td>
 
       <td></td>
 
       <td></td>
 
       <td></td>
 
       <td></td>
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<p>For example:</p>
 
<p>For example:</p>
  
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;∘.=⍨⍳4 ⍝ Identity matrix<br />
+
<apll>
 +
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;×⍨⍳5 ⍝ squares <br/>
 +
1 4 9 16 25<br/>
 +
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;∘.=⍨⍳4 ⍝ Identity matrix<br />
 
1 0 0 0<br />
 
1 0 0 0<br />
 
0 1 0 0<br />
 
0 1 0 0<br />
 
0 0 1 0<br />
 
0 0 1 0<br />
 
0 0 0 1<br />
 
0 0 0 1<br />
 +
</apll>
 +
 +
<apll>
 +
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2*⍨⍳5 ⍝ squares <br/>
 +
1 4 9 16 25<br/>
 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;√+/2*⍨6 2⍴3 4, 5 12, 8 15, 7 24, 20 21, 12 35 ⍝ Pythagorean hypotenuses<br />
 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;√+/2*⍨6 2⍴3 4, 5 12, 8 15, 7 24, 20 21, 12 35 ⍝ Pythagorean hypotenuses<br />
 
5 13 17 25 29 37<br />
 
5 13 17 25 29 37<br />
 
 
</apll>
 
</apll>

Revision as of 11:15, 1 December 2016

Duplicate: Z←f⍨ R      returns R f R.
Commute: Z←L f⍨ R returns R f L.
L and R are arrays.
f is a function.

For example:

      ×⍨⍳5 ⍝ squares
1 4 9 16 25
      ∘.=⍨⍳4 ⍝ Identity matrix
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

      2*⍨⍳5 ⍝ squares
1 4 9 16 25
      √+/2*⍨6 2⍴3 4, 5 12, 8 15, 7 24, 20 21, 12 35 ⍝ Pythagorean hypotenuses
5 13 17 25 29 37