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	<title>Untouchable number - Revision history</title>
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	<updated>2026-04-22T11:35:10Z</updated>
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		<id>https://en.formulasearchengine.com/index.php?title=Untouchable_number&amp;diff=234866&amp;oldid=prev</id>
		<title>115.80.92.106 at 15:42, 1 October 2014</title>
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		<updated>2014-10-01T15:42:47Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Untouchable_number&amp;amp;diff=234866&amp;amp;oldid=234865&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>115.80.92.106</name></author>
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		<title>198.96.34.104: reworded &quot;prime except two&quot; to &quot;odd prime&quot;</title>
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		<updated>2014-02-18T16:04:38Z</updated>

		<summary type="html">&lt;p&gt;reworded &amp;quot;prime except two&amp;quot; to &amp;quot;odd prime&amp;quot;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&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 18:04, 18 February 2014&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-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&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;In [[mathematics]]&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a &lt;/del&gt;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;Poisson superalgebra&#039;&#039;&#039; is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Z&#039;&#039;&#039;&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sub&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/sub&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-[[graded algebra|graded]] generalization &lt;/del&gt;of a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Poisson algebra]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Specifically&lt;/del&gt;, a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Poisson superalgebra &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an (associative) [[superalgebra]] &lt;/del&gt;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A&#039;&#039; with &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Lie superbracket]]&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;Msvcr71.dll is an significant file that assists help Windows process different components of the system including important files. Specifically&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the file is selected to help run corresponding files in the &quot;Virtual C Runtime Library&quot;. These files are important in accessing any settings that support the different applications plus programs inside the system. The msvcr71.dll file fulfills countless significant functions; but it&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s not spared from getting damaged or corrupted. Once the file gets corrupted or damaged, the computer might have &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;difficult time processing and reading components of the system. However, consumers want not panic considering this problem might be solved by following several procedures. And I will show you certain tips about Msvcr71.dll.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Document files allow the consumer to input data, images, tables and other ingredients to enhance the presentation. The only problem with this structure compared to other file kinds such as .pdf for illustration is its ability to be easily editable. This means which anybody viewing the file will change it by accident. Additionally, this file structure is opened by alternative programs yet it does not guarantee that what you see inside the Microsoft Word application can nonetheless become the same whenever we see it using another program. However, it is still preferred by many computer consumers for its ease &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;utilize plus features.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;The &#039;registry&#039; is &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;central database which shops information, settings plus options for the computer&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It&#039;s actually the many normal reason why XP runs slow and should you fix this issue&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;we can create the computer run &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lot faster. The problem &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that the &lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;registry&lt;/ins&gt;&#039; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;shops a lot of settings plus details about a PC... plus because Windows requires to use &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lot of of these settings, any corrupted or damaged ones may straight affect the speed of the program.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Windows errors can be caused by any amount of reasons, however there&#039;s almost always one cause. There&#039;s a hidden part of your program &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is responsible for creating 90% of all Windows mistakes, plus it&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s called the &lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;registry&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. This is the central database for your program and is where your computer shops all its system files plus settings. It&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s a truly important part of Windows&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which is needs to be able to function. However&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it&#039;s furthermore among the largest causes of issues on &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PC.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;There are &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lot of &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//bestregistrycleanerfix.com/tune-up&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;utilities tuneup utilities&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Which one &lt;/ins&gt;is the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;greatest &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;not convenient to be determined&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;But when you desire to stand out &lt;/ins&gt;one &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;amidst &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;multitude you could take into consideration several items. These are features, scanning speed time, total mistakes detected, total mistakes repaired, tech support, Boot time performance and price. According to these items Top Registry Cleaner for 2010 is RegCure&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;S/w connected error handling - If the blue screen bodily memory dump arises after &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;installation &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;w application or a driver it may be that there is system incompatibility&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;By booting into safe mode plus removing the software you are able to fast fix this error. You might equally try out a &quot;program restore&quot; to revert &lt;/ins&gt;to an &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;earlier state&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It is critical which we remove obsolete registry entries from your program regularly, if you need a program to run faster&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which is. If you don&#039;t keep your registry clean&lt;/ins&gt;, a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;time usually come whenever the program can stop working completely&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Then&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the just way &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to reformat &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;difficult drive plus start over!&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A registry cleaner is a program that cleans the registry. The Windows registry constantly gets flooded with junk data, info that has not been removed from uninstalled programs&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;erroneous file organization and alternative computer-misplaced entries. These clean little program software tools are very common nowadays plus you will find quite &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;few superior ones on the Internet&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The wise ones provide you choice to maintain, clean, update, backup, plus scan the System Registry. Whenever it finds supposedly unwelcome elements in it, the registry cleaner lists them plus recommends the consumer to delete or repair these orphaned entries and corrupt keys&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;:&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[\cdot,\cdot] : A\otimes A\to A&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;such &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(&lt;/del&gt;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A&lt;/del&gt;&#039;&#039;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[·&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;·]) is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Lie superalgebra]] and the operator&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;:&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[x,\cdot] : A\to A&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;is &lt;/del&gt;a [&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[superderivation]] of &#039;&#039;A&#039;&#039;&lt;/del&gt;:&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;math&amp;gt;[x,yz] = [x,y]z + (&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1)^{|x||y|}y[x,z&lt;/del&gt;].&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\,&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;A supercommutative Poisson algebra &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one for which &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(associative) product &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[supercommutative algebra|supercommutative]]&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;This is &lt;/del&gt;one &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;possible way of &quot;super&quot;izing &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Poisson algebra&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This gives &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;classical dynamics &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fermion fields and classical spin-1&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2 particles&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The other is &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;define &lt;/del&gt;an &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[antibracket algebra]] instead. This is used in the [[BRST quantization|BRST]] and [[Batalin-Vilkovisky]] formalism&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;== Examples ==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;* If &#039;&#039;A&#039;&#039; is any associative &#039;&#039;&#039;Z&#039;&#039;&#039;&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sub&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/sub&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;graded algebra&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;then&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;defining &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;new product [&lt;/del&gt;.,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.] (which &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;called &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;super-commutator) by [x,y]:=xy-(-1)&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sup&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|x||y|&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/sup&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;yx for any pure graded x&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;y turns &#039;&#039;A&#039;&#039; into &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Poisson superalgebra&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;==See also==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;*[[Poisson supermanifold]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;==References==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;*{{springer|id=p/p110170|title=Poisson algebra|author=Y&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Kosmann-Schwarzbach}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;[[Category:Super linear algebra]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;[[Category:Symplectic geometry]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>198.96.34.104</name></author>
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		<title>en&gt;CsDix: /* External links */ template name update</title>
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		<title>en&gt;Luckas-bot: r2.7.1) (Robot: Adding it:Numero intoccabile</title>
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