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Definition #71498
- Preferred
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| selma'o |
VUhU |
| definition |
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.
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| notes |
S="ro" is default case (making this operator binary or ternary); S must be a set or "ro" (no bare integers); m = 0 is the default case (making this operator binary or ternary); use "mau'au" and "zai'ai" in order to quote f and g each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form
(x1, x2, x3,..., xn,...); thus, notationally, a concrete output of this function, as applied to the aforementioned concrete input tuple, is of form (fa'ai'ai
(f, g, S, m))(x1, x2,..., xn,...). For example, maintaining this notation, if S="ro" and m = 0, then the output is
f (g(x1), g(x2),..., g(xn),...); if S = Set(1, 3, 23) and m = 0, then the output is
f (g(x1), x2, g(x3), x4, x5,..., x21, x22, g(x23), x24, x25,..., xn,...); vel sim. If h is the function output by this expression when m = 0, then for the same inputs (ignoring m), goh is the function output by the same expression but with m = 1. Obviously, in order to be meaningful, the output of each step along the way must be defined. If S is the empty set and g is defined, then the output is just the function f if m = 0. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when S or m is omitted (as being equal to the default "ro" or 0 resp.).
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| created by |
krtisfranks |
| vote information |
1
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| time |
Sun Sep 8 06:07:04 2019 |
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