https://wiki.lojban.io/index.php?action=history&feed=atom&title=pau%27aupau'au - Revision history2026-04-27T23:26:56ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=pau%27au&diff=12388&oldid=prevNalvaizmiku: Import words via API2026-01-13T15:58:43Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
pau'au<br />
==== type ====<br />
experimental cmavo<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Thu Oct 27 04:13:15 2022<br />
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== English ==<br />
=== Definition #73015 - Preferred ===<br />
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==== selma'o ====<br />
VUhU3<br />
==== definition ====<br />
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ternary mekso operator: p-adic valuation; outputs (positive) infinity if <span class="MATH"><i>x</i><sub>1</sub> = 0</span> and, else, outputs sup<span class="MATH">(</span>Set(<span class="MATH"><i>k</i> : <i>k</i></span> is a nonnegative integer, and MATH<br />
$((1 - x_3)x_2 + x_3 p_{x_2})^k$<br />
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<span class="MATH">((1 - <i>x</i><sub>3</sub>)<i>x</i><sub>2</sub> + <i>x</i><sub>3</sub><i>p</i><sub>x<sub>2</sub></sub>)<sup>k</sup></span> divides <span class="MATH"><i>x</i><sub>1</sub>))</span>, where <span class="MATH"><i>p</i><sub>n</sub></span> is the <span class="MATH"><i>n</i></span>th prime (such that <span class="MATH"><i>p</i><sub>1</sub> = 2</span>).<br />
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==== notes ====<br />
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The terbri order here was defined in analogy to "[[de'o|de'o]]". Normally, <span class="MATH"><i>x</i><sub>1</sub></span> should be a rational number, and <span class="MATH"><i>x</i><sub>2</sub></span> should be a positive integer; some generalizations may be possible, though. <span class="MATH"><i>x</i><sub>3</sub></span> is either <span class="MATH">0</span> xor <span class="MATH">1</span>, and indicates/toggles between modes: <span class="MATH"><i>x</i><sub>3</sub> = 0</span> yields the <span class="MATH"><i>x</i><sub>2</sub></span>-adic valuation (even for nonprime <span class="MATH"><i>x</i><sub>2</sub></span>); <span class="MATH"><i>x</i><sub>3</sub> = 1</span> yields the <span class="MATH"><i>p</i><sub>x<sub>2</sub></sub></span>-adic valuation. MATH<br />
$x_2 = 1, x_3 = 0$<br />
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<span class="MATH"><i>x</i><sub>2</sub> = 1, <i>x</i><sub>3</sub> = 0</span> yields positive infinity for any <span class="MATH"><i>x</i><sub>1</sub></span> which is within the domain. If <span class="MATH"><i>x</i><sub>1</sub> = <i>n</i>/<i>m</i></span> and is a rational noninteger number such that gcd<span class="MATH">(<i>n</i>, <i>m</i>) = 1</span>, then pau'au MATH<br />
$(x_1, x_2, x_3) =$<br />
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<span class="MATH">(<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, <i>x</i><sub>3</sub>) =</span> pau'au MATH<br />
$(n, x_2, x_3) -$<br />
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<span class="MATH">(<i>n</i>, <i>x</i><sub>2</sub>, <i>x</i><sub>3</sub>) -</span> pau'au MATH<br />
$(m, x_2, x_3)$<br />
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<span class="MATH">(<i>m</i>, <i>x</i><sub>2</sub>, <i>x</i><sub>3</sub>)</span>. See also: "[[fei'i|fei'i]]", "[[pi'ei'oi|pi'ei'oi]]". This word is often equivalent to or closely related to "[[pei'e'a|pei'e'a]]" (which is, in some ways, more general but also is less flexible with respect to its input).<br />
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==== gloss words ====<br />
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<ul><li>[[natlang/en/exponent of factors|exponent of factors]]</li><li>[[natlang/en/integer exponent|integer exponent]]</li><li>[[natlang/en/maximum exponent of factor|maximum exponent of factor]]</li><li>[[natlang/en/p-adic order|p-adic order]]</li><li>[[natlang/en/p-adic valuation|p-adic valuation]]</li><li>[[natlang/en/prime-logarithm|prime-logarithm]]</li></ul><br />
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==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
1<br />
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==== time ====<br />
Thu Oct 27 05:51:43 2022<br />
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<br/><font size="+1">Examples</font><br />
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=== Etymology ===</div>Nalvaizmiku