Received: from [192.168.123.254] (port=47874 helo=db.digitalkingdom.org) by stodi.digitalkingdom.org with smtp (Exim 4.94) (envelope-from ) id 1kl56V-002Jwe-6f for jbovlaste-admin@lojban.org; Thu, 03 Dec 2020 23:02:09 -0800 Received: by db.digitalkingdom.org (sSMTP sendmail emulation); Fri, 04 Dec 2020 07:02:06 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word fau'i -- By krtisfranks Date: Fri, 4 Dec 2020 07:02:06 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -2.9 (--) X-Spam_score: -2.9 X-Spam_score_int: -28 X-Spam_bar: -- In jbovlaste, the user krtisfranks has edited a definition of "fau'i" in the language "English". Differences: 2,2c2,2 < mekso ternary operator: inverse function of input function $X_1$ with respect to its input $X_2$, taken on branch $X_3$. --- > mekso ternary operator: inverse function of input function $X_1$ with respect to its input $X_2$, taken on branch or restricted domain $X_3$ ("domain" being of $X_1$). 5,5c5,5 < $X_3$ often omitted due to obviousness (or due to lack of need/due to well-definition) or convention. $X_1$ should be a function supplied in "{zay'au}" quotes; that function itself should be at least unary and the input against which the inverse is being taken in an n-ary $X_1$ is $X_2$. $X_2$ should technically be a input slot index or domain (or subspace/projection thereof), but a named and non-evaluated dummy variable symbol can be supplied if the slot ordering or domain terms (vel sim.) are not well-specified. See also: "{fau'e}" (this word acts as a better-specified case of iteration order $n=-1$ for "fau'e"). --- > The output of this function is itself a function of the same arity as $X_1$. $X_3$ often omitted due to obviousness (or due to lack of need/due to well-definition) or convention. $X_1$ should be a function supplied in "{zau'au}" quotes; that function itself should be at least unary and the input against which the inverse is being taken in an n-ary $X_1$ is $X_2$. $X_2$ should technically be a input slot index or domain (or subspace/projection thereof), but a named and non-evaluated dummy variable symbol can be supplied if the slot ordering or domain terms (vel sim.) are not well-specified. Because the output is a function, it can itself (that is: the output's self) have an input; use "{bai'i'i}" or an equivalent thereof for this purpose in most situations. For example, if $f(x, y, z) = w, g = $fau'i$(f, 2), v = (x, y, z),$ and $u = $bai'i'i$(v, 2, w) = (x, w, z)$, then $g(u) = f_2^{-1}(x, w, z) = y$. In English notation, "fau'i$(f, n)$" might be notated as "inv$(f, n)$". See also: "{fau'e}" (this word acts as a better-specified case of iteration order $n=-1$ for "fau'e"). Old Data: Definition: mekso ternary operator: inverse function of input function $X_1$ with respect to its input $X_2$, taken on branch $X_3$. Notes: $X_3$ often omitted due to obviousness (or due to lack of need/due to well-definition) or convention. $X_1$ should be a function supplied in "{zay'au}" quotes; that function itself should be at least unary and the input against which the inverse is being taken in an n-ary $X_1$ is $X_2$. $X_2$ should technically be a input slot index or domain (or subspace/projection thereof), but a named and non-evaluated dummy variable symbol can be supplied if the slot ordering or domain terms (vel sim.) are not well-specified. See also: "{fau'e}" (this word acts as a better-specified case of iteration order $n=-1$ for "fau'e"). Jargon: Gloss Keywords: Word: inverse function, In Sense: Place Keywords: New Data: Definition: mekso ternary operator: inverse function of input function $X_1$ with respect to its input $X_2$, taken on branch or restricted domain $X_3$ ("domain" being of $X_1$). Notes: The output of this function is itself a function of the same arity as $X_1$. $X_3$ often omitted due to obviousness (or due to lack of need/due to well-definition) or convention. $X_1$ should be a function supplied in "{zau'au}" quotes; that function itself should be at least unary and the input against which the inverse is being taken in an n-ary $X_1$ is $X_2$. $X_2$ should technically be a input slot index or domain (or subspace/projection thereof), but a named and non-evaluated dummy variable symbol can be supplied if the slot ordering or domain terms (vel sim.) are not well-specified. Because the output is a function, it can itself (that is: the output's self) have an input; use "{bai'i'i}" or an equivalent thereof for this purpose in most situations. For example, if $f(x, y, z) = w, g = $fau'i$(f, 2), v = (x, y, z),$ and $u = $bai'i'i$(v, 2, w) = (x, w, z)$, then $g(u) = f_2^{-1}(x, w, z) = y$. In English notation, "fau'i$(f, n)$" might be notated as "inv$(f, n)$". See also: "{fau'e}" (this word acts as a better-specified case of iteration order $n=-1$ for "fau'e"). Jargon: Gloss Keywords: Word: inverse function, In Sense: Place Keywords: You can go to to see it.