mekso string operator (ternary): find-and-replace; in string/text/word/sequence X1 formally replace X2 (ordered tuple of terms to be replaced) with X3 (ordered tuple of terms to be respectively substituted)
mekso operator: in ordered tuple/list/vector/sequence X1, replace the X2th entry with term X3 of appropriate type, and leave all other entries untouched (optional: where the index for the very first/leading/header entry is X4).
ternary mekso operator: x1th Bergelson multiplicative interval with exponents bounded from above by function x2 and with sequence of shifts x3, where exponents belong to set x4
mekso operator/function terminator (in Polish notation): inserts exactly enough "{boi}"'s consecutively so as to terminate the most recently uttered operator/function in a mekso expression
mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
mekso at-most-4-ary operator: integer lattice ball; the set of all points belonging to the intersection of Zn with the closure of the ball that is centered on X1 and has radius X2 in metric X3, where Z is the set of all integers and where, for any set A and non-negative integer n,
An is the set of all n-tuples such that each coordinate/entry/term belongs to A, and where the dimensionality n = X4..
mekso ternary operator: positive super-logarithm; the super-logarithm (inverse operator of hyper-operator with respect to "height" of power tower) of a with base b and of order c-2.
mekso n-ary ordered operator: structure creator/ordered tuple, 'endow'; the structure formed by underlying set X1 (as) endowed with element, order, quoted operator, etc. X2, X3, ...
mekso binary operator: extract substructure/underlying set/endowing operator; the substructure (general sense; includes just operator, order, set, etc.) of X1 (structure; explicitly given by {du'a'e}) which is formed by collecting the ith entries of that {du'a'e}-tuple in order together into their own {du'a'e}-tuple (or by extracting them naked into the ambient environment if X2 is a singleton) for all i in set X2
mekso binary operator: left-handed vectorial cross product (ordered input), -a \times b = b \times a (if using right-hand convention - notice the negative sign/operator or order).
mekso k-ary operator, for natural k and 1 < k < 5: ordered input (f, g, S, m) where f and g are functions, S is a set of positive integers or "ro" (="all"), and m is 0 or 1 (as a toggle); output is a function equivalent to the function f as applied to an input ordered tuple with g applied to the entries/terms with indices in S (or to all entries/terms if S="ro") if m=0, or g left-composed with the same if m=1.
mekso ternary operator: inverse function of input function X1 with respect to its input X2, taken on branch or restricted domain X3 ("domain" being of X1).
mekso variable-arity (at most ternary) operator: number of prime divisors of number X1, counting with or without multiplicity according to the value X2 (1 xor 0 respectively; see note for equality to -1 and for default value), in structure X3.
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.
mekso unary operator: converts a string of digits which includes {pi} to the same string of digits without {pi}; if {pi} is not present in the original/input string, the output is identical
mekso operator, variable arity - algebraic structure order of X1; OR: order
of/(size of) period of element X1 in algebraic structure X2 under operator/of type X3
mekso, at-most-5-ary operator: a rounding function; ordered input list is (x,n,t,m,b) and the output is sgn(x) bt roundn (b(-t) abs(x)), with rounding preference n and where the fractional part of b(-t) abs(x) being equal to 1/2 causes the roundn ( ) function to map b(-t) abs(x) to the nearest integer of form 2Z+m, for base b (determined by context if not explicitly input) and some integer Z (determined by context).
mekso string operator (n-ary): formal right-concatenation; X1 + X, where Xi is a string/word/text/character/letteral/lerfu/quoted utterance (quote appropriately iff necessary; preserve and be careful about the use-vs.-mention distinction) for all i.
non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: X2 ^C; binary: X1\setminusX.
mathematical/logical/mekso ternary operator: μ (mu) operator: outputs the most extreme extended-natural number that satisfies relationship/predicate A, where extremeness is bounded by B and of a version determined by C; error output is -1
mekso ternary operator: the generalized incomplete (factorial-extending) Pi function; for input (X1, X this word outputs the definite integral of t^X1 e^-t with respect to t from X2 to X3 (see notes for default values).
mathematical/mekso binary operator: the zero/identity-element/(primitive (-))constant operator; outputs the identity-element of structure A (contextless default: the additive group of integers) regardless of the input value of B (except blank or ill-defined values)
ternary mekso operator: p-adic valuation; outputs (positive) infinity if x1 = 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x3)x divides x1)), where pn is the nth prime (such that p1 = 2).
mekso operator: power set - produces the set of all subsets of set X1 that are of (any) size (that is) X2 [a nonnegative integer or transfinite/infinite number; default: su'o no].
n-ary mekso operator: for an input of ordered list of ordered pairs ((X1, Y, it outputs formal generalized rational function (x - X1)^Y in the adjoined indeterminate (here: x).
mekso at-most-3-ary operator: convert to polynomial; X1 (ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate X2 under ordering rule X3 (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)
mekso binary operator: generate span; outputs span(X1, X= spanX; set of all (finite) sums of terms of form c v, where v is an element of algebraic structure X1 (wherein scalar multiplication and summation is defined), and c is a scalar belonging to ring X2.
ternary mekso/mathematical operator: radical; for input (x,y,z), it outputs the largest y-th-power-free product of prime divisors of x in structure (ring) z.
mekso (2 or 3)-ary operator: maximum/minimum/extreme element; ordered list of extreme elements of the set underlying ordered set/structure X1 in direction X2 of list length X3 (default: 1)
mekso binary operator: del, nabla, quabla, partial-derivative vector/tensor operator; outputs the functional-valued formal-covector (or analog thereof) of partial derivatives with respect to X1 (tensor in the same format and order), each degree X2 (default: 1).
mekso unary or binary operator: ordered inputs (n, b) where n and b are nonnegative integers and b > 1; output is the ultimate digital root of n in base-b.
8-ary mekso operator: the X1th nonnegative sum of X2 mutually-distinct perfect X3th-powers (i.e.: of integers) in X4 mutually truly-distinct ways, requiring exactly X5 terms to be negative in each sum (counting with(out^X6) multiplicity), requiring exactly X7 terms to be repeated between sums (counting with(out^X8) multiplicity), according to the usual ordering of the integers.
mekso ternary operator: Knuth up-arrow notation: a \uparrow \dots \uparrow b of order/with c-2 arrows ("\uparrow") initially, evaluated from right to left; the cth hyperoperator on a by b.
6-ary mekso/mathematical operator: Heaviside function/step/Theta function of a, of order b, in structure c, using distribution d, within approximated limit e, with value f_b at 0
4-ary mekso operator: Taylor expansion/polynomial term; for ordered input (X1, X, output is the X3th Taylor polynomial term of at-least-X3-smooth function X2 which was expanded around point X4 and which is evaluated at point X1, namely (1/(X3!)) × (D^X.
binary mekso operator: Let the inputs X1 and X2 be sets in the same universal set O; then the result of this operator applied to them is X1^c
\cup X, where for any A \subseteq O, Ac = O \setminus A.
binary mekso operator: Let the inputs X1 and X2 be sets in the same universal set O; then the result of this operator applied to them is X1^c
\cap X, where for any A \subseteq O, Ac = O \setminus A.
binary mekso operator: for ordered list X1, this word outputs the same ordered list except the indices/subscripts have been relabelled/redefined/reindexed according to rule X2 (see notes).
mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
x1=c1 (zo) is a cmavo with a predicate role or semantic structure which expresses predicate x2=b1 (quote/du'u) between arguments x3=b3 (ordered list), the said cmavo being of form or in category/class x4=c2 in/and belonging to language/dialect x5=c3.
x1 is a scalar in structure/set x2 with properties (potentially including magnitude, etc. in a given metric and coordinate system) x3; x1 is a simple number; x1 is a number that lacks
x1 is a formal polynomial with coefficients x2 (ordered list) of degree x3 (li; nonnegative integer) over structure/ring x4 (to which coefficients x2 all belong) and in indeterminant x5.
x1 abstractly pertains to an exponential/root/logarithmic relationship between the elements of x2 (ordered pair) which are related via concrete relationship x3.