https://wiki.lojban.io/index.php?action=history&feed=atom&title=po%27i%27oi 2026-04-28T03:14:19Z Revision history for this page on the wiki MediaWiki 1.45.3 https://wiki.lojban.io/index.php?title=po%27i%27oi&diff=12987&oldid=prev 2026-01-13T16:03:52Z

<p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> po&#039;i&#039;oi<br /> ==== type ====<br /> experimental cmavo<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Sat Apr 30 17:59:28 2016<br />  <br /> == English ==<br /> === Definition #68642 - Preferred ===<br />  <br /> ==== selma&#039;o ====<br /> VUhU<br /> ==== definition ====<br /> <br /> mekso at-most-3-ary operator: convert to polynomial; &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; (ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; under ordering rule &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; (default for finite list: the first entry is the coefficient of the highest-degree term and each subsequent entry is the next lesser-degree coefficient via counting by ones and wherein the last entry is the constant term)<br /> <br /> ==== notes ====<br /> <br /> In English, there is no good way to distinguish between &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; + 2&lt;i&gt;x&lt;/i&gt;&lt;/span&gt; as a function and as a number; typical notation would demand that it is a number but abuse must be adopted since no easy alternative exists for its expression as a function (such as when it is being defined; mapping notation is one of the best options, but is cumbersome). Lojban now allows for such functionality: just apply this word to the ordered list (1,2,0) and do not fill the second terbri (&lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;: the indeterminate). This word can also be viewed as creating an object in a ring. Termination of the list is extremely important; under normal interpretations, list entries can themselves have operations applied internally; moreover, multiple indetermimates can be introduced by careful application of this word to a list wherein each entry is itself treated as a polynomial. The last entry in &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; must be &#039;constant&#039; term (when understood as a function), so care must be taken to explicitly mention an appropriate number of zeroes. See also: &quot;[[cpolinomi&#039;a|cpolinomi&#039;a]]&quot;, &quot;[[po&#039;i&#039;ei|po&#039;i&#039;ei]]&quot;.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/convert list to polynomial|convert list to polynomial]]&lt;/li&gt;&lt;li&gt;[[natlang/en/polynomial coefficient list convert|polynomial coefficient list convert]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Thu Mar 9 22:02:56 2023<br /> <br /> <br /> <br /> &lt;br/&gt;&lt;font size=&quot;+1&quot;&gt;Examples&lt;/font&gt;<br /> &lt;hr/&gt;<br /> &lt;dl&gt;<br /> &lt;/dl&gt;<br /> <br /> === Etymology ===</div>

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