at-most-3-ary mekso operator: "integer exponent" for X_{1} divided by X_{2} in algebraic structure X_{3}

Produces the maximum integer n such that X_{2 ^n | X} in/according to the rules of X_{3}. X_{1} and X_{2} each must be nonzero and not units. Context or explicit specification elsewhere may make X_{3} 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 (X_{3 }= (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): p^{n} divides r in N)), where "P" denotes the set of primes in the unique factorization domain of integers.

- pau'au
- ternary mekso operator: p-adic valuation; outputs (positive) infinity if x
_{1 }= 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x_{3)x}divides x_{1))}, where p_{n}is the nth prime (such that p_{1 }= 2).