# se'au VUhU experimental cmavo

mathematical quinary operator; big operator: left sequence notation/converter - operator a, sequence b defined as a function on index/argument/variable/parameter c, in set d, under ordering e

Produces the left application of the operation/function a=• on sequence b(c), the terms of which are functions evaluated at (possibly dummy) values c (multi-index), where each c belongs to set d (at the values of which the function b is evaluated), operation a being applied thereto in order e (rule prescription; specifies order of c's running through d; note that the application is from the left). The steps at which c's are taken can be specified by d or by taking complicated (evaluated) expressions z(c) instead of c as arguments of b. Notice that e affects both c (or z(c)) directly as well as b (less directly) by being established on d. Output is in the format (for example: scalar, tensor, function, etc.) that the operation a=• yields. If b is a constant (at least with respect to the arguments c being ranged over), then the operator a is taken being applied to b for a number of times equal to the cardinality of d (and, technically, in the order specified by e). If d is explicitly created via use of ce'o, then the order is from the first term uttered to the last term uttered, as uttered; e need not be specified (if it is, it overrides the order of utterance). For Sigma/series summation notation (si'i), a=+, for Pi multiplication notation a=×, for functional power/iterated composition of functions a=∘, for the Cartesian product of sets a=× (preferred to "exponentiation of sets" notation like An). mau'au and zai'ai will be necessary for the proper use of this word (particularly for specifying a and e); e will be specified explicitly (possibly elsewhere) and/or via zoi'ai. See also: ma'o'e.

## In notes:

fau'e (exp!)
iterated function left-composition with self: f∘f∘...∘f, n times.
fi'au
mekso operator: continued fraction, Kettenbruch notation; for ordered input (X1, X, where: X1 is an ordered pair of functions and X2 is a free or dummy variable/input/index which ranges through set X3 in order(ing) X4, the result is K(X for Kettenbruch notation K.
kei'au
mekso operator: finite result set derived from/on set A with/due to operator/function B under ordering of application C
mau'au
mekso: conversion of operator/function to operand
pi'u'e (exp!)
mekso n-ary operator: generate ordered tuple/list from inputs; pi'u'e(x1, x= (x1, x, pi'u'e(x1, x= (x1, x, etc.
te'au
iterated Cartesian product with self: A × A × ... × A, n times.
zoi'ai
non-mekso quote/name substitution for ordered collection of prescriptions, descriptions, definitions, etc.