Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Wed, 26 Oct 2022 21:15:10 -0700 Received: from [192.168.123.254] (port=38162 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1onuIN-007ET4-De for jbovlaste-admin@lojban.org; Wed, 26 Oct 2022 21:15:09 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Thu, 27 Oct 2022 04:15:07 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word pau'au -- By krtisfranks Date: Thu, 27 Oct 2022 04:15:07 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -1.9 (-) X-Spam_score: -1.9 X-Spam_score_int: -18 X-Spam_bar: - In jbovlaste, the user krtisfranks has edited a definition of "pau'au" in the language "English". Differences: 2,2c2,2 < ternary mekso operator: p-adic valuation; outputs infinity ($+\infty$) if $x_1 = 0$ and, else, outputs $\operatorname{sup}({k \in \mathbb{Z}^{+} \cup {0}: (x_2 * (1 - x_3) + p_{x_2} * x_3)^k$ divides $ x_1})$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). --- > ternary mekso operator: p-adic valuation; outputs infinity (+∞) if $x_1 = 0$ and, else, outputs sup$({k \in \mathbb{Z}^{+} \cup {0}: (x_2 * (1 - x_3) + p_{x_2} * x_3)^k$ divides $ x_1})$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). 5,5c5,5 < Terbri order in analog to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer. $x_3$ is either $0$ xor $1$ and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields infinity ($+\infty$) for any $x_1$. If $x_1 = n/m \in mathbb{Q}$\$\mathbb{Z}: \operatorname{gcd}(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. --- > Terbri order in analog to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer. $x_3$ is either $0$ xor $1$ and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields infinity ($+\infty$) for any $x_1$. If $x_1 = n/m \in mathbb{Q}$\$\mathbb{Z}:$ gcd$(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. 11,11d10 < Word: p-adic valuation, In Sense: \n12a12,12 \n> Word: p-adic valuation, In Sense: Old Data: Definition: ternary mekso operator: p-adic valuation; outputs infinity ($+\infty$) if $x_1 = 0$ and, else, outputs $\operatorname{sup}({k \in \mathbb{Z}^{+} \cup {0}: (x_2 * (1 - x_3) + p_{x_2} * x_3)^k$ divides $ x_1})$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). Notes: Terbri order in analog to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer. $x_3$ is either $0$ xor $1$ and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields infinity ($+\infty$) for any $x_1$. If $x_1 = n/m \in mathbb{Q}$\$\mathbb{Z}: \operatorname{gcd}(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. Jargon: Gloss Keywords: Word: p-adic valuation, In Sense: Word: p-adic order, In Sense: Word: prime-logarithm, In Sense: Place Keywords: New Data: Definition: ternary mekso operator: p-adic valuation; outputs infinity (+∞) if $x_1 = 0$ and, else, outputs sup$({k \in \mathbb{Z}^{+} \cup {0}: (x_2 * (1 - x_3) + p_{x_2} * x_3)^k$ divides $ x_1})$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). Notes: Terbri order in analog to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer. $x_3$ is either $0$ xor $1$ and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields infinity ($+\infty$) for any $x_1$. If $x_1 = n/m \in mathbb{Q}$\$\mathbb{Z}:$ gcd$(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. Jargon: Gloss Keywords: Word: p-adic order, In Sense: Word: p-adic valuation, In Sense: Word: prime-logarithm, In Sense: Place Keywords: You can go to to see it.