fau'a FAUhA experimental cmavo

Convert operator to being entrywise.

Applied to an operator by immediately following it; breaks the symmetry which that operator may have had: the first argument of the operator is to be a tensor or (multidimensional) list, or a set, or something with many internal terms, entries, elements, components, etc; the subsequent arguments of the operator are arbitrary. The result is to apply the operator with the subsequent arguments to each term, entry, elements, etc. of the first argument individually. For example, for matrix A=((1, 2), (3, 4)), A+(fau'a)10 = ((11, 12),(13, 14)) and A^2 = ((7, 10), (15, 22)); however, A^(fau'a)2 = ((1, 4), (9, 16)); likewise, sin(A) = A - (1/3)A^3 + (1/5)A^5 - ..., but sin(fau'a)(A) = ((sin(1), sin(2)), (sin(3), sin(4))), which is meant to show the distribution of the sin() function to each entry of A, although it also happens to be equivalent to applying the Taylor expansion to A via "fau'a" as well. Caution must be used: matrix addition or scalar multiplication of matrices already have this distributional property, so this word is not needed in those cases; in fact, A+(fau'a)A would yield ((1+A, 2+A), (3+A, 4+A)), which is nonsensical (because, without "fau'a", the addition of a scalar entry to a matrix is undefined).

In definition:

Iteratively applies "fau'a" to each resultant operator until all operators resolve.