Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Thu, 09 Mar 2023 14:03:00 -0800 Received: from [192.168.123.254] (port=41368 helo=jiten.lojban.org) by 8612a944938c with smtp (Exim 4.94.2) (envelope-from ) id 1paOLh-0005ky-6v for jbovlaste-admin@lojban.org; Thu, 09 Mar 2023 14:02:59 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Thu, 09 Mar 2023 22:02:57 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word po'i'oi -- By krtisfranks Date: Thu, 9 Mar 2023 22:02:57 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -1.0 (-) X-Spam_score: -1.0 X-Spam_score_int: -9 X-Spam_bar: - In jbovlaste, the user krtisfranks has edited a definition of "po'i'oi" in the language "English". Differences: 5,5c5,5 < In English, there is no good way to distinguish between $x^2 + 2x$ 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 ($X_2$: 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 $X_1$ must be 'constant' term (when understood as a function), so care must be taken to explicitly mention an appropriate number of zeroes. See also: {cpolinomi'a}. --- > In English, there is no good way to distinguish between $x^2 + 2x$ 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 ($X_2$: 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 $X_1$ must be 'constant' term (when understood as a function), so care must be taken to explicitly mention an appropriate number of zeroes. See also: "{cpolinomi'a}", "{po'i'ei}". Old Data: Definition: mekso at-most-3-ary operator: convert to polynomial; $X_1$ (ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate $X_2$ under ordering rule $X_3$ (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) Notes: In English, there is no good way to distinguish between $x^2 + 2x$ 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 ($X_2$: 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 $X_1$ must be 'constant' term (when understood as a function), so care must be taken to explicitly mention an appropriate number of zeroes. See also: {cpolinomi'a}. Jargon: Gloss Keywords: Word: convert list to polynomial, In Sense: Word: polynomial coefficient list convert, In Sense: Place Keywords: New Data: Definition: mekso at-most-3-ary operator: convert to polynomial; $X_1$ (ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate $X_2$ under ordering rule $X_3$ (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) Notes: In English, there is no good way to distinguish between $x^2 + 2x$ 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 ($X_2$: 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 $X_1$ must be 'constant' term (when understood as a function), so care must be taken to explicitly mention an appropriate number of zeroes. See also: "{cpolinomi'a}", "{po'i'ei}". Jargon: Gloss Keywords: Word: convert list to polynomial, In Sense: Word: polynomial coefficient list convert, In Sense: Place Keywords: You can go to to see it.