x1 is an n-ary operator/map which is distributive/linear/homomorphic in or over or from space/structure x2, mapping to space or structure x3, thereby producing a new space/structure x4 which is the 'union' of x2 and x3 endowed with x1; x1 distributes over/through all of the operators of x2.
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.
x1 is an eigenvalue (or zero) of linear transformation/square matrix x2, associated with/'owning' all vectors in generalized eigenspace x3 (implies neither nondegeneracy nor degeneracy; default includes the zero vector) with 'eigenspace-generalization' power/exponent x4 (typically and probably by cultural default will be 1), with algebraic multiplicity (of eigenvalue) x5
x1 (li; often but not necessarily an integer) is a multiple of x2 (li; often but not necessarily an integer) by some integer, namely x3 (li; MUST be an integer in the structure; possibly, more than one input may be valid), in algebraic structure x4.
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-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)
x1 is a mathematical structure defined on underlying structure/set/parts x2 with properties/rules/relations/operands/functions/substructures x3 in mathematics x4.
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.
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).
x1 is a strict/proper sub-x2 [structure] in/of x3; x2 is a structure and x1 and x3 are both examples of that structure x2 such that x1 is entirely contained within x3 (where containment is defined according to the standard/characteristics/definition of x2; but in any case, no member/part/element that belongs to x1 does not also belong to x3), but there is some member/part/element of x3 that does not belong to x1 in the same way.