View source for fau'i

==== valsi ====
fau'i
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Mon Apr 20 04:33:11 2020
 
== English ==
=== Definition #71920 - Preferred ===
 
==== selma'o ====
VUhU
==== definition ====

mekso ternary operator: inverse function of input function <span class="MATH"><i>X</i><sub>1</sub></span> with respect to its input <span class="MATH"><i>X</i><sub>2</sub></span>, taken on branch or restricted domain <span class="MATH"><i>X</i><sub>3</sub></span> ("domain" being of <span class="MATH"><i>X</i><sub>1</sub></span>).

==== notes ====

The output of this function is itself a function of the same arity as <span class="MATH"><i>X</i><sub>1</sub></span>. <span class="MATH"><i>X</i><sub>3</sub></span> often omitted due to obviousness (or due to lack of need/due to well-definition) or convention. <span class="MATH"><i>X</i><sub>1</sub></span> should be a function supplied in "[[zau'au|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 <span class="MATH"><i>X</i><sub>1</sub></span> is <span class="MATH"><i>X</i><sub>2</sub></span>. <span class="MATH"><i>X</i><sub>2</sub></span> 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|bai'i'i]]" or an equivalent thereof for this purpose in most situations. For example, if  MATH
 $f(x,y,z)=w,g=fau'i(f,2),v=(x,y,z)$
 
<span class="MATH"><i>f</i> (<i>x</i>, <i>y</i>, <i>z</i>) = <i>w</i>, <i>g</i> = <i>fau'i</i>(<i>f</i>, 2), <i>v</i> = (<i>x</i>, <i>y</i>, <i>z</i>)</span>, and  MATH
 $u=bai'i'i(v,2,w)=(x,w,z)$
 
<span class="MATH"><i>u</i> = <i>bai'i'i</i>(<i>v</i>, 2, <i>w</i>) = (<i>x</i>, <i>w</i>, <i>z</i>)</span>, then  MATH
 $g(u)=f^<a class="undefined" href="../dict/-1?bg=1;langidarg=2">-1</a>_2(x,w,z)=y$
 
<span class="MATH"><i>g</i>(<i>u</i>) = <i>f</i><sup>-1</sup><sub>2</sub>(<i>x</i>, <i>w</i>, <i>z</i>) = <i>y</i></span>. In English notation, " MATH
 $fau'i(f,n)$
 
<span class="MATH"><i>fau'i</i>(<i>f</i>, <i>n</i>)</span>" might be notated as "<span class="MATH"><i>inv</i>(<i>f</i>, <i>n</i>)</span>". See also: "[[fau'e|fau'e]]" (this word acts as a better-specified case of iteration order <span class="MATH"><i>n</i> = - 1</span> for "fau'e").

==== gloss words ====

<ul><li>[[natlang/en/inverse function|inverse function]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
2
     
==== time ====
Fri Nov 26 09:40:16 2021



<br/><font size="+1">Examples</font>
<hr/>
<dl>
</dl>

=== Etymology ===