pei'e'a VUhU experimental cmavo

at-most-3-ary mekso operator: "integer exponent" for X1 divided by X2 in algebraic structure X3

Produces the maximum integer n such that X2 ^n | X in/according to the rules of X3. X1 and X2 each must be nonzero and not units. Context or explicit specification elsewhere may make X3 unnecessary. For natural numbers, the Wolfram Language calls this "IntegerExponent" (if we ignore the arity and the default specifications; but the argument order is preserved). In this case (X3 = (N, +, ×), where "N " denotes the set of all natural numbers (positive integers)), this function can be usefully restricted to f:(N Exclude Set(1)) Union P -> N Union Set(0), (r,p) -> max( Set(n in N Union Set(0): pn divides r in N)), where "P" denotes the set of primes in the unique factorization domain of integers.

In notes:

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).