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	<id>https://wiki.nars2000.org/index.php?action=history&amp;feed=atom&amp;title=Without</id>
	<title>Without - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://wiki.nars2000.org/index.php?action=history&amp;feed=atom&amp;title=Without"/>
	<link rel="alternate" type="text/html" href="https://wiki.nars2000.org/index.php?title=Without&amp;action=history"/>
	<updated>2026-05-08T05:34:08Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.38.7</generator>
	<entry>
		<id>https://wiki.nars2000.org/index.php?title=Without&amp;diff=3177&amp;oldid=prev</id>
		<title>Sudleyplace at 23:25, 15 April 2018</title>
		<link rel="alternate" type="text/html" href="https://wiki.nars2000.org/index.php?title=Without&amp;diff=3177&amp;oldid=prev"/>
		<updated>2018-04-15T23:25:29Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:25, 15 April 2018&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l28&quot;&gt;Line 28:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 28:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;p&amp;gt;This feature is implemented by an internal magic function:&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;p&amp;gt;This feature is implemented by an internal magic function:&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;apll&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;{del}&amp;amp;nbsp;&lt;/del&gt;Z←L #DydTilde R&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/apll&amp;gt;&amp;lt;br /&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;apll&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;pre&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;apll&amp;gt;&lt;/del&gt;[1]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&lt;/del&gt;Z←(~L∊R)/L&amp;lt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;apll&amp;gt;&amp;lt;br /&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;    ∇ &lt;/ins&gt;Z←L #DydTilde R&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;apll&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;{del}&lt;/del&gt;&amp;lt;/apll&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;[1] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;  &lt;/ins&gt;Z←(~L∊R)/L&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;    ∇&lt;/ins&gt;&amp;lt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pre&lt;/ins&gt;&amp;gt;&amp;lt;/apll&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Sudleyplace</name></author>
	</entry>
	<entry>
		<id>https://wiki.nars2000.org/index.php?title=Without&amp;diff=245&amp;oldid=prev</id>
		<title>Sudleyplace at 01:23, 8 May 2008</title>
		<link rel="alternate" type="text/html" href="https://wiki.nars2000.org/index.php?title=Without&amp;diff=245&amp;oldid=prev"/>
		<updated>2008-05-08T01:23:22Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 21:23, 7 May 2008&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l4&quot;&gt;Line 4:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 4:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;     &amp;lt;table border=&amp;quot;0&amp;quot; cellpadding=&amp;quot;5&amp;quot; cellspacing=&amp;quot;0&amp;quot; summary=&amp;quot;&amp;quot;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;     &amp;lt;table border=&amp;quot;0&amp;quot; cellpadding=&amp;quot;5&amp;quot; cellspacing=&amp;quot;0&amp;quot; summary=&amp;quot;&amp;quot;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;     &amp;lt;tr&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;     &amp;lt;tr&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;       &amp;lt;td&amp;gt;&amp;lt;apll&amp;gt;Z←L~R&amp;lt;/apll&amp;gt;&amp;lt;/td&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;       &amp;lt;td &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;valign=&amp;quot;top&amp;quot;&lt;/ins&gt;&amp;gt;&amp;lt;apll&amp;gt;Z←L~R&amp;lt;/apll&amp;gt;&amp;lt;/td&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;       &amp;lt;td&amp;gt;&amp;lt;/td&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;       &amp;lt;td&amp;gt;&amp;lt;/td&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;       &amp;lt;td&amp;gt;&amp;lt;/td&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;       &amp;lt;td&amp;gt;&amp;lt;/td&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Sudleyplace</name></author>
	</entry>
	<entry>
		<id>https://wiki.nars2000.org/index.php?title=Without&amp;diff=188&amp;oldid=prev</id>
		<title>Sudleyplace: New page: &lt;table border=&quot;1&quot; cellpadding=&quot;5&quot; cellspacing=&quot;0&quot; rules=&quot;none&quot; summary=&quot;&quot;&gt; &lt;tr&gt;   &lt;td&gt;     &lt;table border=&quot;0&quot; cellpadding=&quot;5&quot; cellspacing=&quot;0&quot; summary=&quot;&quot;&gt;     &lt;tr&gt;       &lt;td&gt;&lt;apll&gt;Z←L~R&lt;/a...</title>
		<link rel="alternate" type="text/html" href="https://wiki.nars2000.org/index.php?title=Without&amp;diff=188&amp;oldid=prev"/>
		<updated>2008-04-13T19:54:02Z</updated>

		<summary type="html">&lt;p&gt;New page: &amp;lt;table border=&amp;quot;1&amp;quot; cellpadding=&amp;quot;5&amp;quot; cellspacing=&amp;quot;0&amp;quot; rules=&amp;quot;none&amp;quot; summary=&amp;quot;&amp;quot;&amp;gt; &amp;lt;tr&amp;gt;   &amp;lt;td&amp;gt;     &amp;lt;table border=&amp;quot;0&amp;quot; cellpadding=&amp;quot;5&amp;quot; cellspacing=&amp;quot;0&amp;quot; summary=&amp;quot;&amp;quot;&amp;gt;     &amp;lt;tr&amp;gt;       &amp;lt;td&amp;gt;&amp;lt;apll&amp;gt;Z←L~R&amp;lt;/a...&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;table border=&amp;quot;1&amp;quot; cellpadding=&amp;quot;5&amp;quot; cellspacing=&amp;quot;0&amp;quot; rules=&amp;quot;none&amp;quot; summary=&amp;quot;&amp;quot;&amp;gt;&lt;br /&gt;
&amp;lt;tr&amp;gt;&lt;br /&gt;
  &amp;lt;td&amp;gt;&lt;br /&gt;
    &amp;lt;table border=&amp;quot;0&amp;quot; cellpadding=&amp;quot;5&amp;quot; cellspacing=&amp;quot;0&amp;quot; summary=&amp;quot;&amp;quot;&amp;gt;&lt;br /&gt;
    &amp;lt;tr&amp;gt;&lt;br /&gt;
      &amp;lt;td&amp;gt;&amp;lt;apll&amp;gt;Z←L~R&amp;lt;/apll&amp;gt;&amp;lt;/td&amp;gt;&lt;br /&gt;
      &amp;lt;td&amp;gt;&amp;lt;/td&amp;gt;&lt;br /&gt;
      &amp;lt;td&amp;gt;&amp;lt;/td&amp;gt;&lt;br /&gt;
      &amp;lt;td&amp;gt;returns a subset of &amp;lt;apll&amp;gt;L&amp;lt;/apll&amp;gt; consisting of those elements in &amp;lt;apll&amp;gt;L&amp;lt;/apll&amp;gt; which do not occur in &amp;lt;apll&amp;gt;R&amp;lt;/apll&amp;gt;.&amp;lt;/td&amp;gt;&lt;br /&gt;
    &amp;lt;/tr&amp;gt;&lt;br /&gt;
    &amp;lt;/table&amp;gt;&lt;br /&gt;
  &amp;lt;/td&amp;gt;&lt;br /&gt;
&amp;lt;/tr&amp;gt;&lt;br /&gt;
&amp;lt;tr&amp;gt;&lt;br /&gt;
  &amp;lt;td&amp;gt;&amp;lt;apll&amp;gt;L&amp;lt;/apll&amp;gt; is a scalar or vector, else signal &amp;lt;apll&amp;gt;RANK ERROR&amp;lt;/apll&amp;gt;.&amp;lt;/td&amp;gt;&lt;br /&gt;
&amp;lt;/tr&amp;gt;&lt;br /&gt;
&amp;lt;tr&amp;gt;&lt;br /&gt;
  &amp;lt;td&amp;gt;&amp;lt;apll&amp;gt;R&amp;lt;/apll&amp;gt; is an arbitrary array.&amp;lt;/td&amp;gt;&lt;br /&gt;
&amp;lt;/tr&amp;gt;&lt;br /&gt;
&amp;lt;tr&amp;gt;&lt;br /&gt;
  &amp;lt;td&amp;gt;&amp;lt;apll&amp;gt;Z&amp;lt;/apll&amp;gt; is a vector identical to &amp;lt;apll&amp;gt;(~L∊R)/L&amp;lt;/apll&amp;gt;.&amp;lt;/td&amp;gt;&lt;br /&gt;
&amp;lt;/tr&amp;gt;&lt;br /&gt;
&amp;lt;tr&amp;gt;&lt;br /&gt;
  &amp;lt;td&amp;gt;The result is sensitive to &amp;lt;apll&amp;gt;⎕CT&amp;lt;/apll&amp;gt;.&amp;lt;/td&amp;gt;&lt;br /&gt;
&amp;lt;/tr&amp;gt;&lt;br /&gt;
&amp;lt;/table&amp;gt;&lt;br /&gt;
&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;p&amp;gt;This feature is implemented by an internal magic function:&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;apll&amp;gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;{del}&amp;amp;nbsp;Z←L #DydTilde R&amp;lt;/apll&amp;gt;&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;apll&amp;gt;[1]&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;Z←(~L∊R)/L&amp;lt;/apll&amp;gt;&amp;lt;br /&amp;gt;&lt;br /&gt;
&amp;lt;apll&amp;gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;{del}&amp;lt;/apll&amp;gt;&lt;/div&gt;</summary>
		<author><name>Sudleyplace</name></author>
	</entry>
</feed>