https://wiki.lojban.io/index.php?action=history&feed=atom&title=cpolinomi%27a cpolinomi'a - Revision history 2026-05-05T23:36:42Z Revision history for this page on the wiki MediaWiki 1.45.3 https://wiki.lojban.io/index.php?title=cpolinomi%27a&diff=3282&oldid=prev Nalvaizmiku: Import words via API 2026-01-13T14:38:53Z <p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> cpolinomi&#039;a<br /> ==== type ====<br /> fu&#039;ivla<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Tue Jan 21 19:08:15 2014<br />  <br /> == English ==<br /> === Definition #44334 - Preferred ===<br />  <br /> ==== definition ====<br /> x&lt;sub&gt;1&lt;/sub&gt; is a formal polynomial with coefficients x2 (ordered list) of degree x&lt;sub&gt;3&lt;/sub&gt; (li; nonnegative integer) over structure/ring x&lt;sub&gt;4&lt;/sub&gt; (to which coefficients x&lt;sub&gt;2&lt;/sub&gt; all belong) and in indeterminant x&lt;sub&gt;5&lt;/sub&gt;.<br /> ==== notes ====<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; must be greater than or equal to the number of entries in &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;; if these two values are not equal, then the explicitly mentioned entries of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; are the values of the coefficients as will be described next, starting with the most important one; all the following coefficients (which are not explicitly mentioned) are [[xo&#039;ei|xo&#039;ei]] (taking appropriate values) until and including once the constant term&#039;s coefficient (when understood as a function) is reached. If &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; is presented as an ordered list, the entries represent the &#039;coefficients&#039; of the particular polynomial and are specified in the order such that the &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt;th entry/term is the &lt;span class=&quot;MATH&quot;&gt;(&lt;i&gt;n&lt;/i&gt; - &lt;i&gt;i&lt;/i&gt; + 1)&lt;/span&gt;th &#039;coefficient&#039;, for all positive integers &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt; which are less than or equal to &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt; + 1&lt;/span&gt;, where the ordering of &#039;coefficients&#039; is determined by the exponent of the indeterminate associated therewith (when treated as a function); thus, the last entry is the constant term (when treated as a function), the penultimate term is the coefficient of the argument of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;5&lt;/sub&gt;&lt;/span&gt; (when treated as a function), and the first term is the coefficient of the argument of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;5&lt;/sub&gt;&lt;/span&gt; exponentiated by &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; (which is the degree &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; of the 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;); in other words, the &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt;th entry of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; (where indexing of the ordered list starts at &lt;span class=&quot;MATH&quot;&gt;1&lt;/span&gt;) is the coefficient of MATH<br /> $x^&lt;a class=&quot;undefined&quot; href=&quot;../dict/(n-i%2b1)?bg=1;langidarg=2&quot;&gt;(n-i+1)&lt;/a&gt;$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sup&gt;(n-i+1)&lt;/sup&gt;&lt;/span&gt;, where &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;5&lt;/sub&gt; = &lt;i&gt;x&lt;/i&gt;&lt;/span&gt; is the indeterminate. &quot;[[ze&#039;ai&#039;au|ze&#039;ai&#039;au]]&quot; enables for reversal of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; so that the first-uttered term is the constant, the next-uttered term is the coefficient of the linear term, ..., and the last ((n+1)st) term is the coefficient of the most-significant term in the polynomial (&lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sup&gt;n&lt;/sup&gt;&lt;/span&gt;). See also: &quot;[[tefsujme&#039;o|tefsujme&#039;o]]&quot; ([[brivla|brivla]]: polynomial function), &quot;[[po&#039;i&#039;oi|po&#039;i&#039;oi]]&quot; (basically, the mekso equivalent to this word), &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/coefficient|coefficient ; polynomial]]&lt;/li&gt;&lt;li&gt;[[natlang/en/coefficient ring|coefficient ring ; of polynomial]]&lt;/li&gt;&lt;li&gt;[[natlang/en/indeterminant|indeterminant ; of formal polynomial]]&lt;/li&gt;&lt;li&gt;[[natlang/en/polynomial|polynomial ; formal, ring element (not as: a function or a funcion evaluated at a particular input value)]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== place keywords ====<br /> <br /> 3.<br /> [[natlang/en/degree|degree ; polynomial]]<br /> &lt;br/&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 2<br /> <br /> ==== time ====<br /> Thu Mar 9 22:04:38 2023<br /> <br /> [[comments.html?valsi=17928;definition=44334|[View<br /> Comments For This Definition]]] <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> Nalvaizmiku