- bai'i
- 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)
- be'ei'oi
- ternary mekso operator: x
_{1}th Bergelson multiplicative interval with exponents bounded from above by function x_{2}and with sequence of shifts x_{3}, where exponents belong to set x_{4} - bei'u'i
- unary mekso operator: nth Bernoulli number B
_{n}of the second kind (B_{1 }= +1/2 = >0). - boi'ai
- unary mekso operator: immediately convert number into a single digit.
- ca'ei'a
- Unary mekso operator: unit vector/normalization of the argument (vector) X.
- ca'o'e
- mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
- ca'oi
- binary operator: complex number from argument and phase, (r, \phi) \mapsto r e
^{i \phi} - ci'ai'u
- unary mex operator: n-set; maps a nonnegative integer 'a' to the set \1, \dots ,a\ (the intersection of the set of all natural numbers with the closed ordered interval [1,a] such that a geq 1).
- ci'au'i
- mensonge at-most-3-ary operator: integer lattice ball; the set of all points belonging to the intersection of Z
^{n}with the closure of the ball that is centered on X_{1}and has radius X_{2}in metric X_{3}, where Z is the set of all integers and where, for any set A and non-negative integer n, A^{n}is the set of all n-tuples such that each coordinate/entry/term belongs to A - ci'o'au
- mekso operator (binary): projection function; the Bth term/entry ("element") of tuple A
- cu'au'ei
- mekso binary/unary operator: multinomial coefficient/binomial coefficient/choose
- da'a'au
- mekso operatory: prime mark append
- dei'au'o
- mekso binary operator: Lambert product-log W function; W(a, b)
- di'ei'o'au
- mathematical ternary operator: Dirichlet convolution (a×b)(c)
- du'a'e
- mekso n-ary ordered operator: structure creator/ordered tuple, 'endow'; the structure formed by underlying set X
_{1}(as) endowed with element, order, quoted operator, etc. X_{2}, X_{3}, ... - du'a'o
- mekso binary operator: extract substructure/underlying set/endowing operator; the substructure (general sense; includes just operator, order, set, etc.) of X
_{1}(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 X_{2}is a singleton) for all i in set X_{2} - du'ei
- 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).
- fa'ai
- mathematical ordered n-ary operator: (pointwise) functional left composition; X
_{1 \circ X}. - fa'ai'ai
- 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.
- fa'au
- mathematical unary operator: map notation
- fe'ei
- binary mekso operator: divided by (fraction): a/(b...)
- fei'i
- mekso variable arity (at most ternary) operator: number of prime divisors of number A, counting with or without multiplicity according to the value B (1 or 0 respectively), in structure C
- ga'ai
- unary mekso operator: Lorentz-Einstein gamma factor +1/((1-(|X|
^{2))}for input X. - gau'a
- mekso (no-more-than-4-ary) operator: Gaussian function f(x, a, b, c) = c e
^{-((x-a)}. - gu'au'i
- 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
- je'e'e
- mekso operator: assoviated Legendre polynomial in a with unassociated order b and associated order c
- ji'e'ai
- mekso unary operator: determinant, det(A)
- ji'i'u
- mekso at-most-4-ary operator: a rounding function; ordered input list is (x,n,m,t) and the output is b
^{(-t) ×}round(b^{t × x}), with rounding preference n and where the fractional part of b^{t × x}being 1/2 causes the function to map b^{t × x}to the nearest integer of form 2Z+m, for base b and an integer Z determined by context - joi'i
- mekso string operator (n-ary): formal left-concatenation; X
_{1+X}, where X_{i}is a string/word/text - ku'au'a
- mekso (n+1)-ary operator: q-analog converter - the ath analog of b (quoted operator) applied to operands c, d, ...
- ma'au
- Binary mekso operator: uniform probability A(X
_{2)u(X}for input (X_{1,X}where X_{1}is a number and X_{2}is a set or space. (See notes for details). - mai'u
- unary mekso operator: signum function
- ma'o'e
- mathematical operator: vague/elliptical/general/generic operator
- me'ei'o
- mekso n-ary operator: interleave sequences
- mu'ai'au
- 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
- mu'au
- unary mekso operator: measure of the complement; 1 - x
_{1}. - nei'au
- unary mekso operator: (-1)
^{x} - no'au'au
- 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)
- pau'a'u
- mekso operator: part of number/projection (one sense); the X2 part of X1
- pau'ei
- mekso operator: power set - produces the set of all subsets of set A that are of (any) size (that is) b [a nonnegative integer or transfinite/infinite number]
- pei'e'a
- at-most-3-ary mekso operator: "integer exponent" for X
_{1}divided by X_{2}in algebraic structure X_{3} - pi'au'e
- mekso ternary operator: extract digit from number; X
_{2}nd macrodigit/term of number/tuple X_{1}when X_{1}is expressed in base/basis X_{3}. - pi'ei
- mathematical/mekso binary operator: vector or function inner product over a field; the inner product of A and B over field C
- pi'ei'au
- mathematical ternary operator: not-greater-prime-counting function
- pi'ei'oi
- mathematical ternary operator: prime-generating function
- po'i'oi
- mekso at-most-3-ary operator: convert to polynomial; X
_{1}(ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate X_{2}under ordering rule X_{3}(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) - ra'i'e
- 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.
- rai'i
- mekso (2 or 3)-ary operator: maximum/minimum/extreme element; ordered list of extreme elements of the set underlying ordered set/structure X
_{1}in direction X_{2}of list length X_{3}(default: 1) - sau'i
- mekso n-ary operator: reciprocal of the sum of the reciprocal of each of X
_{1}, X_{2}, ..., X_{n}(for any natural number n); 1/((1/X_{1) + (1/X}. - se'i'a'o
- unary mathematical operator: identity function id(a) = a
- si'oi'e
- n-ary mekso operator: Logistical growth, sigmoid function; \bigg( \frac(X
_{2)(1+e^(-X}. - su'i'e
- mekso unary operator: digital addition.
- su'i'o
- 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.
- tai'i'e
- mekso unary operator: Kleene star - X1*
- te'au'u
- 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.
- te'i'ai
- 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
- tei'au
- 4-ary mekso operator: Taylor expansion/polynomial term; for ordered input (X
_{1, X}, output is the X_{3}th Taylor polynomial term of at-least-X_{3}-smooth function X_{2}which was expanded around point X_{4}and which is evaluated at point X_{1}, namely (1/(X_{3!)) × (D^X}. - te'o'a
- unary mekso operator: natural exponentiation operator exp, where exp(a) = e
^{a \forall a}. - to'ei'au
- binary mathematical operator: Jordan totient function J
_{a(b)} - vau'i
- mekso n-ary operator: reciprocal of the successive ordered-difference of the reciprocal of each of x
_{1, x}; id est output is ((\dots ((x_{1^-1 - x} - vei'u
- binary mekso operator: mod(ulus)/remainder; X
_{1}\% X_{2}, \,\,\, X_{1}(mod(X_{2})). - vi'oi'au
- mekso unary operator: the set of all fixed points of function a
- vo'au'u
- quaternary mathematical operator: (left) convolution (a★b)(c) in structure d
- xa'ai
- mekso operator: the bth branch of the (possibly multivalued) function a
- xo'ei
- unary mekso operator: produces a string of n consecutive "xo'e"'s, treated as digits (concatenated into a single string of digits)
- xo'e'o'ei
- At-most-unary mekso operator: like {xo'ei} but for selma'o XOhEhOhE, rather than just PA
- za'ei
- mekso binary operator: right-handed vectorial cross product (ordered input), a×b
- zi'a'o
- mathematical operator: the empty/null [one sense]/trivial [one sense]/blank operator
- cia'o'e
- mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
- xua'ai
- mekso operator: the bth branch of the (possibly multivalued) function a
- cu'a
- unary mathematical operator: absolute value/norm |a|.
- de'o
- binary mathematical operator: logarithm; [log/ln a to base b]; default base 10 or e.
- fa'i
- unary mathematical operator: reciprocal; multiplicative inverse; [1/a].
- fe'a
- binary mathematical operator: nth root of; inverse power [a to the 1/b power].
- fe'i
- n-ary mathematical operator: divided by; division operator; [(((a / b) / c) / ...)].
- fu'u
- n-ary mathematical operator: elliptical/unspecified mathematical expression (mex) operator.
- ge'a
- mathematical operator: null mathematical expression (mex) operator (used in >2-ary ops).
- gei
- trinary mathematical operator: order of magnitude/value/base; [b * (c to the a power)].
- ju'u
- binary mathematical operator: number base; [a interpreted in the base b].
- ne'o
- unary mathematical operator: factorial; a!.
- pa'i
- binary mathematical operator: ratio; [the ratio of a to b].
- pi'a
- n-ary mathematical operator: operands are vectors to be treated as matrix rows.
- pi'i
- n-ary mathematical operator: times; multiplication operator; [(((a * b) * c) * ...)].
- re'a
- unary mathematical operator: matrix transpose/dual; A*.
- ri'o
- trinary mathematical operator: [integral of a with respect to b over range c].
- sa'i
- n-ary mathematical operator: operands are vectors to be treated as matrix columns.
- sa'o
- trinary mathematical operator: [derivative of a with respect to b of degree c].
- si'i
- trinary mathematical operator: [sigma summation of a using variable b over range c].
- su'i
- n-ary mathematical operator: plus; addition operator; [(((a + b) + c) + ...)].
- te'a
- binary mathematical operator: to the power; exponential; [a to the b power].
- va'a
- unary mathematical operator: additive inverse; [- a].
- vu'u
- n-ary mathematical operator: minus; subtraction operator; [(((a - b) - c) - ...)].
- su'ifa'uvu'u
- mekso operator: plus or minus with order important, (((a±b)±c)±...±z)
- su'ijavu'u
- mekso operator: plus or minus, (((a±b)±c)±...±z)
- bai'ei
- unary mathematical operator: successor/augment/increment (by one), succ(a) = a++ = a+1
- cu'ai
- binary mathematical operator: vector norm/magnitude of vector a in structure (normed vector space) b
- de'au'u
- 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.
- fe'au'u
- mekso ternary operator: positive super-root; the bth super-root (inverse operator of hyper-operator with respect to base) of a of order c-2.
- gu'ai
- binary operator: left group action g.x
- jau'au
- unary mathematical operator: length/number of components/terms of/in object/array/formal string/sequence/word/text in some alphabet/base/basis which includes each digit; number of digits/components/entries
- ka'au
- mekso unary operator: cardinality (#, | |)
- ne'oi
- unary operator: primorial a#
- pau'oi
- unary mathematical operator: predecessor/diminish/decrement (by one), \operatornamepred(a) = a-- = a-1
- ru'ei
- n-ary operator: n-ary magma/group/ring operator a*b = ab`
- zei'i'au
- unary mekso operator: (analytically continued) Riemann zeta function zeta(z), for complex-valued input z.

- kau'ai
- Microdigit-spanning endianness binary-toggle.
- kau'au
- Macrodigit-spanning endianness binary-toggle.
- ma'oi
- selma'o quote; quotes a word (a cmavo) and uses it to name a selma'o.
- ma'oi'e
- Like "ma'oi" but outputs the officially-designated/canonical sub-selma'o (if any) to which the immediately following and quoted word (cmavo) belongs, otherwise outputting the whole relevant selma'o in fashion equivalent to "ma'oi".
- noi'a'u
- PA nonrestrictive/incidental relative clause; attaches to a PA number/numeral/digit with the ke'a referring to that PA number/numeral/digit.
- poi'a'u
- PA restrictive relative clause; attaches to a PA number/numeral/digit with the ke'a referring to that PA number/numeral/digit.
- te'au
- iterated Cartesian product with self: A × A × ... × A, n times.
- xau'e
- symbol string to number/variable
- enfa
- x
_{1}abstractly pertains to an exponential/root/logarithmic relationship between the elements of x_{2}(ordered pair) which are related via concrete relationship x_{3}. - mekseia
- x
_{1}is a part of Lojban text representing rule 'mex-operator' according to the first edition of the book 'The Complete Lojban Language'.