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At - Revision history
2026-05-08T05:34:13Z
Revision history for this page on the wiki
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WikiSysop: /* Variable v. Jot */
2023-12-04T22:16:27Z
<p><span dir="auto"><span class="autocomment">Variable v. Jot</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:16, 4 December 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l89">Line 89:</td>
<td colspan="2" class="diff-lineno">Line 89:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td>For example:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td>For example:</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Replace all items of <apll>R</apll>:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Replace all <ins style="font-weight: bold; text-decoration: none;">of the </ins>items of <apll>R<ins style="font-weight: bold; text-decoration: none;"></apll> with <apll>¯1</ins></apll>:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><apll><pre></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><apll><pre></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ¯1@∘⍳2 3</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ¯1@∘⍳2 3</div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Function v. Variable===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Function v. Variable===</div></td></tr>
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WikiSysop
https://wiki.nars2000.org/index.php?title=At&diff=3850&oldid=prev
WikiSysop at 22:14, 4 December 2023
2023-12-04T22:14:09Z
<p></p>
<a href="https://wiki.nars2000.org/index.php?title=At&diff=3850&oldid=3848">Show changes</a>
WikiSysop
https://wiki.nars2000.org/index.php?title=At&diff=3848&oldid=prev
WikiSysop: Created page with "==At Derived Functions== <p>The dyadic At operator is used to index assign into an array <apll>R</apll>, returning as the result the changed array. There are four separate cases, depending upon whether the two operands are Variables or Functions. The design of this operator is taken directly from the corresponding feature in Dyalog APL.</p> ===Variable v. Variable=== <table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""> <tr> <td> <table bor..."
2023-11-28T02:24:21Z
<p>Created page with "==At Derived Functions== <p>The dyadic At operator is used to index assign into an array <apll>R</apll>, returning as the result the changed array. There are four separate cases, depending upon whether the two operands are Variables or Functions. The design of this operator is taken directly from the corresponding feature in Dyalog APL.</p> ===Variable v. Variable=== <table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""> <tr> <td> <table bor..."</p>
<p><b>New page</b></p><div>==At Derived Functions==<br />
<br />
<p>The dyadic At operator is used to index assign into an array <apll>R</apll>, returning as the result the changed array. There are four separate cases, depending upon whether the two operands are Variables or Functions. The design of this operator is taken directly from the corresponding feature in Dyalog APL.</p><br />
<br />
===Variable v. Variable===<br />
<br />
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""><br />
<tr><br />
<td><br />
<table border="0" cellpadding="5" cellspacing="0" summary=""><br />
<tr><br />
<td valign="top"><apll>Z←<i>a</i>@<i>b</i> R</apll></td>+<br />
</tr><br />
<tr><br />
<td>Replaces the <apll><i>b</i></apll> items of <apll>R</apll> with <apll><i>a</i></apll>, where <apll><i>a</i></apll> and <apll><i>b</i></apll> are variables.</td><br />
</tr><br />
</table><br />
</td><br />
</tr><br />
<tr><br />
<td>For example:<br />
Replace the 1st and last characters in a string with a string:<br />
<apll><pre><br />
(⊂'abra')@(1 5)'scads!'<br />
abra cad abra !</pre></apll><br />
</td><br />
</tr><br />
<tr><br />
<td>Replace the diagonal elements of a matrix:<br />
<apll><pre><br />
'abcd'@(2/¨⍳4)4 4⍴⍳16<br />
a 2 3 4<br />
5 b 7 8<br />
9 10 c 12<br />
13 14 15 d</pre></apll></td><br />
</tr><br />
<tr><br />
<td><p>This case is implemented via the anonymous function <apll>{A←⍵ ⋄ 1≥≡A:A⊣A[⊃⍵⍵⌷¨⊂⍳⍴A]←⍺⍺ ⋄ A[⍵⍵]←⍺⍺ ⋄ A}</apll>.</p></td><br />
</tr><br />
</table><br />
&nbsp;<br />
===Function v. Variable===<br />
<br />
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""><br />
<tr><br />
<td><br />
<table border="0" cellpadding="5" cellspacing="0" summary=""><br />
<tr><br />
<td valign="top"><apll>Z←{L} <i>f</i>@<i>b</i> R</apll></td><br />
<br />
</tr><br />
<tr><br />
<td>Replaces the <apll><i>b</i></apll> items of <apll>R</apll> with <apll><i>f</i></apll> applied to each replaced item, where <apll>{L}</apll> is an optional left argument to <apll><i>f</i></apll>, <apll><i>f</i></apll> is a function, and <apll><i>b</i></apll> is a variable.</td><br />
</tr><br />
</table><br />
</td><br />
</tr><br />
<tr><br />
<td>For example:<br />
Replace the diagonal elements of a matrix with their reciprocals:<br />
<apll><pre><br />
÷@(2/¨⍳4)4 4⍴⍳16<_x/><br />
1 2 3 4<br />
5 1<_r/>6 7 8<br />
9 10 1<_r/>11 12<br />
13 14 15 1<_r/>16<br />
</pre></apll><br />
</td><br />
</tr><br />
<tr><br />
<td>Replace the diagonal elements of a matrix with their duplicates:<br />
<apll><pre><br />
2/¨@(2/¨⍳4)4 4⍴⍳16<br />
1 1 2 3 4 <br />
5 6 6 7 8 <br />
9 10 11 11 12 <br />
13 14 15 16 16<br />
</pre</apll></td><br />
</tr><br />
<tr><br />
<td><p>This case is implemented via the anonymous function <apll>{⍺←⊢ ⋄ A←⍵ ⋄ 1≥≡A:A⊣A[B]←⍺ ⍺⍺ A[B]⊣B←⊃⍵⍵⌷¨⊂⍳⍴A ⋄ A[⍵⍵]←⍺ ⍺⍺ A[⍵⍵] ⋄ A}</apll>.</p></td><br />
</tr><br />
</table><br />
&nbsp;<br />
===Variable v. Function===<br />
<br />
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""><br />
<tr><br />
<td><br />
<table border="0" cellpadding="5" cellspacing="0" summary=""><br />
<tr><br />
<td valign="top"><apll>Z←<i>a</i>@<i>g</i> R</apll></td><br />
</tr><br />
<tr><br />
<td>When the Boolean-valued result of <apll><i>g R</i></apll> is <apll>1</apll>, replace the corresponding element of <apll>R</apll> with the corresponding element of <apll><i>a</i></apll>, where <apll><i>a</i></apll> is a variable and <apll><i>g</i></apll> is a function.</td><br />
</tr><br />
</table><br />
</td><br />
</tr><br />
<tr><br />
<td>For example:<br />
Replace the prime numbers in R with a character:<br />
<apll><pre><br />
'π'@{0π⍵}4 4⍴⍳16<br />
1 π π 4<br />
π 6 π 8<br />
9 10 π 12<br />
π 14 15 16</pre></apll></td><br />
</tr><br />
<tr><br />
<td><p>This case is implemented via the anonymous function <apll>{A←⍵ ⋄ A[⍸⍵⍵ A]←⍺⍺ ⋄ A}</apll>.</p></td><br />
</tr><br />
</table><br />
&nbsp;<br />
===Function v. Function===<br />
<br />
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""><br />
<tr><br />
<td><br />
<table border="0" cellpadding="5" cellspacing="0" summary=""><br />
<tr><br />
<td valign="top"><apll>Z←{L} <i>f</i>@<i>g</i> R</apll></td><br />
</tr><br />
<tr><br />
<td>When the Boolean-valued result of <apll><i>g</i> R</apll> is <apll>1</apll>, replace the corresponding element of <apll>R</apll> with <apll><i>f</i></apll> applied to the same element, where <apll>{L}</apll> is an optional left argument to <apll><i>f</i></apll>, <apll><i>f</i></apll> and <apll><i>g</i></apll> are functions.</td><br />
</tr><br />
</table><br />
</td><br />
</tr><br />
<tr><br />
<td>For example:<br />
Replace composite numbers with their factors:<br />
<apll><pre><br />
π¨@{~0π⍵}4 4⍴⍳16<br />
1 2 3 2 2 <br />
5 2 3 7 2 2 2 <br />
3 3 2 5 11 2 2 3 <br />
13 2 7 3 5 2 2 2 2<br />
</pre></apll></td><br />
</tr><br />
<tr><br />
<td><p>This case is implemented via the anonymous function <apll>{⍺←⊢ ⋄ A←⍵ ⋄ B←⍸⍵⍵ A ⋄ A[B]←⍺ ⍺⍺ A[B] ⋄ A}</apll>.</p></td><br />
</tr><br />
</table></div>
WikiSysop