Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Sat, 12 Nov 2022 12:44:02 -0800 Received: from [192.168.123.254] (port=45734 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1otxM7-008XIW-Jx for jbovlaste-admin@lojban.org; Sat, 12 Nov 2022 12:44:02 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Sat, 12 Nov 2022 20:43:59 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word ne'o'o -- By krtisfranks Date: Sat, 12 Nov 2022 20:43:59 +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 "ne'o'o" in the language "English". Differences: 2,2c2,2 < mekso quaternary operator – Pochhammer symbol: with/for input $(X_1, X_2, X_3, X_4)$, this word/function outputs $\prod_{k = 0}^{X_2 - 1} (X_1 + (-1)^{X_3} X_4 k)$; by default, $X_4 = 1$ unless explicitly defined otherwise. --- > mekso quaternary operator – Pochhammer symbol: with/for input $(X_1, X_2, X_3, X_4)$, this word/function outputs $\prod_{k = 0}^{X_2 - 1} (X_1 + (-1)^{1 - X_3} X_4 k)$; by default, $X_4 = 1$ unless explicitly defined otherwise. 5,5c5,5 < For the basic definition, all inputs (especially those which are not $X_1$) should be nonnegative integers; $X_3$ can be further restricted to $0$ (for the rising factorial) and $1$ (for the falling factorial); $X_4 > 0$ will be typical. $X_2 < 1$ yields the empty product, which is typically defined by convention to be $1$, regardless of all other inputs. $X_2$ is the number of terms in the aforementioned defining product and interacts with $X_4$ in somewhat-complicated ways; be careful to avoid multiplying by nonpositive numbers unless such is actually desired (which may break certain recursive formulas); in order to avoid negative terms, enforce that $X_2 < 1 +$ min$($Set$(1, X_1 \% X_4)) + ((X_1 - (X_1 \% X_4))/X_4)$, where: "$\%$" denotes the modulus/remainder (see: "{vei'u}") of its left-hand/first input (here: $X_1$) wrt/when integer-dividing it by its right-hand/second input (here: $X_4$); recall: $x \% y$ in $[0, y)$ for all real numbers $x$ and $y: y > 0$. Also, $X_4 = 1$ by default. See also: "{ne'o}", "{ne'oi}". --- > For the basic definition, all inputs (especially those which are not $X_1$) should be nonnegative integers; $X_3$ can be further restricted to $0$ (for the falling factorial) and $1$ (for the rising factorial); $X_4 > 0$ will be typical. $X_2 < 1$ yields the empty product, which is typically defined by convention to be $1$, regardless of all other inputs. $X_2$ is the number of terms in the aforementioned defining product and interacts with $X_4$ in somewhat-complicated ways; be careful to avoid multiplying by nonpositive numbers unless such is actually desired (which may break certain recursive formulas); in order to avoid negative terms, enforce that $X_2 < 1 +$ min$($Set$(1, X_1 \% X_4)) + ((X_1 - (X_1 \% X_4))/X_4)$, where: "$\%$" denotes the modulus/remainder (see: "{vei'u}") of its left-hand/first input (here: $X_1$) wrt/when integer-dividing it by its right-hand/second input (here: $X_4$); recall: $x \% y$ in $[0, y)$ for all real numbers $x$ and $y: y > 0$. Also, $X_4 = 1$ by default. See also: "{ne'o}", "{ne'oi}". Old Data: Definition: mekso quaternary operator – Pochhammer symbol: with/for input $(X_1, X_2, X_3, X_4)$, this word/function outputs $\prod_{k = 0}^{X_2 - 1} (X_1 + (-1)^{X_3} X_4 k)$; by default, $X_4 = 1$ unless explicitly defined otherwise. Notes: For the basic definition, all inputs (especially those which are not $X_1$) should be nonnegative integers; $X_3$ can be further restricted to $0$ (for the rising factorial) and $1$ (for the falling factorial); $X_4 > 0$ will be typical. $X_2 < 1$ yields the empty product, which is typically defined by convention to be $1$, regardless of all other inputs. $X_2$ is the number of terms in the aforementioned defining product and interacts with $X_4$ in somewhat-complicated ways; be careful to avoid multiplying by nonpositive numbers unless such is actually desired (which may break certain recursive formulas); in order to avoid negative terms, enforce that $X_2 < 1 +$ min$($Set$(1, X_1 \% X_4)) + ((X_1 - (X_1 \% X_4))/X_4)$, where: "$\%$" denotes the modulus/remainder (see: "{vei'u}") of its left-hand/first input (here: $X_1$) wrt/when integer-dividing it by its right-hand/second input (here: $X_4$); recall: $x \% y$ in $[0, y)$ for all real numbers $x$ and $y: y > 0$. Also, $X_4 = 1$ by default. See also: "{ne'o}", "{ne'oi}". Jargon: Gloss Keywords: Word: ascending factorial, In Sense: Word: ascending sequential product, In Sense: Word: descending factorial, In Sense: Word: descending sequential product, In Sense: Word: factorial power, In Sense: Word: falling factorial, In Sense: Word: falling sequential product, In Sense: Word: lower factorial, In Sense: Word: partial factorial, In Sense: Word: partial n-tuple factorial, In Sense: Word: Pochhammer, In Sense: Word: Pochhammer factorial, In Sense: Word: Pochhammer function, In Sense: Word: Pochhammer polynomial, In Sense: Word: Pochhammer symbol, In Sense: Word: rising factorial, In Sense: Word: rising sequential product, In Sense: Word: upper factorial, In Sense: Place Keywords: New Data: Definition: mekso quaternary operator – Pochhammer symbol: with/for input $(X_1, X_2, X_3, X_4)$, this word/function outputs $\prod_{k = 0}^{X_2 - 1} (X_1 + (-1)^{1 - X_3} X_4 k)$; by default, $X_4 = 1$ unless explicitly defined otherwise. Notes: For the basic definition, all inputs (especially those which are not $X_1$) should be nonnegative integers; $X_3$ can be further restricted to $0$ (for the falling factorial) and $1$ (for the rising factorial); $X_4 > 0$ will be typical. $X_2 < 1$ yields the empty product, which is typically defined by convention to be $1$, regardless of all other inputs. $X_2$ is the number of terms in the aforementioned defining product and interacts with $X_4$ in somewhat-complicated ways; be careful to avoid multiplying by nonpositive numbers unless such is actually desired (which may break certain recursive formulas); in order to avoid negative terms, enforce that $X_2 < 1 +$ min$($Set$(1, X_1 \% X_4)) + ((X_1 - (X_1 \% X_4))/X_4)$, where: "$\%$" denotes the modulus/remainder (see: "{vei'u}") of its left-hand/first input (here: $X_1$) wrt/when integer-dividing it by its right-hand/second input (here: $X_4$); recall: $x \% y$ in $[0, y)$ for all real numbers $x$ and $y: y > 0$. Also, $X_4 = 1$ by default. See also: "{ne'o}", "{ne'oi}". Jargon: Gloss Keywords: Word: ascending factorial, In Sense: Word: ascending sequential product, In Sense: Word: descending factorial, In Sense: Word: descending sequential product, In Sense: Word: factorial power, In Sense: Word: falling factorial, In Sense: Word: falling sequential product, In Sense: Word: lower factorial, In Sense: Word: partial factorial, In Sense: Word: partial n-tuple factorial, In Sense: Word: Pochhammer, In Sense: Word: Pochhammer factorial, In Sense: Word: Pochhammer function, In Sense: Word: Pochhammer polynomial, In Sense: Word: Pochhammer symbol, In Sense: Word: rising factorial, In Sense: Word: rising sequential product, In Sense: Word: upper factorial, In Sense: Place Keywords: You can go to to see it.