mai'u'ei VUhU3 experimental cmavo

mekso unary operator: Levi-Civita symbol; for input n-tuple (a1, a ... , an), where n is a strictly positive integer, the output is \varepsilona, where \varepsilon is the Levi-Civita symbol under the convention of mapping (1, 2, ..., n) to 1.

If any at least two elements of the input tuple are mutually equal (id est: if there exists i and j which are strictly positive integers which do not exceed n such that ai = aj, where the input tuple is as defined supra), then the output is 0; else, the output is sgn((a1, a ... , an)), where the input to the sgn function there is a permutation denoted in one-line permutation notation. This format is somewhat consistent with index notation in tensor calculus, but treats the indices as ordered entries of a tuple. More generally, the Levi-Civita symbol may be defined for any function f which maps space S to S; in such case, the input could be f instead of the aforementioned tuple. Covariant and contravariant Levi-Civita tensors can also be defined. See also: "mai'u'e", "mai'u".


In notes:

mai'u (exp!)
unary mekso operator: signum function