View source for po'i'ei

==== valsi ====
po'i'ei
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Thu Mar  9 21:59:28 2023
 
== English ==
=== Definition #73169 - Preferred ===
 
==== selma'o ====
VUhU3
==== definition ====

<span class="MATH"><i>n</i></span>-ary mekso operator: for an input of ordered list of ordered pairs  MATH
 $((X_1, Y_1), (X_2, Y_2), (X_3, Y_3), ..., (X_n, Y_n))$
 
<span class="MATH">((<i>X</i><sub>1</sub>, <i>Y</i><sub>1</sub>),(<i>X</i><sub>2</sub>, <i>Y</i><sub>2</sub>),(<i>X</i><sub>3</sub>, <i>Y</i><sub>3</sub>),...,(<i>X</i><sub>n</sub>, <i>Y</i><sub>n</sub>))</span>, it outputs formal generalized rational function  MATH
 $(x - X_1)^{Y_1} (x - X_2)^{Y_2} (x - X_3)^{Y_3} ... (x - X_n)^{Y_n}$
 
<span class="MATH">(<i>x</i> - <i>X</i><sub>1</sub>)<sup>Y<sub>1</sub></sup>(<i>x</i> - <i>X</i><sub>2</sub>)<sup>Y<sub>2</sub></sup>(<i>x</i> - <i>X</i><sub>3</sub>)<sup>Y<sub>3</sub></sup>...(<i>x</i> - <i>X</i><sub>n</sub>)<sup>Y<sub>n</sub></sup></span> in the adjoined indeterminate (here: <span class="MATH"><i>x</i></span>).

==== notes ====

<span class="MATH"><i>n</i></span> may be infinite, under the condition that the function is well-defined. In the definition, adjacency of terms denotes multiplication in the relevant algebraic structure. If there is an <span class="MATH"><i>i</i></span> such that <span class="MATH"><i>Y</i><sub>i</sub></span> is omitted, then <span class="MATH"><i>Y</i><sub>i</sub> = 1</span> by default. For any <span class="MATH"><i>i</i></span>, there is no constraint on the values which may be taken by <span class="MATH"><i>X</i><sub>i</sub></span> or <span class="MATH"><i>Y</i><sub>i</sub></span>. See also: "[[po'i'oi|po'i'oi]]".

==== gloss words ====

<ul><li>[[natlang/en/convert list to rational function|convert list to rational function]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1
     
==== time ====
Thu Mar  9 22:02:25 2023



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=== Etymology ===