| Under | u&.v mv mv mv |
|
The verb u &.v is equivalent to the composition u & v except that the verb obverse to v is applied to the result for each cell. That is (subject to the monadic rank of v),
u&.v y ↔ vi u v y where vi is the obverse of v .
The obverse is normally the inverse, as discussed
more fully under the power conjunction ^: .
|
3 +&.^. 4 Inverse of natural log is the exponential
12
(^.^:_1) (^.3)+(^.4)
12
(<b), <|. b=: 1 2 3 ; 2 3 5 7 ; 'abcde'
+---------------------+---------------------+
|+-----+-------+-----+|+-----+-------+-----+|
||1 2 3|2 3 5 7|abcde|||abcde|2 3 5 7|1 2 3||
|+-----+-------+-----+|+-----+-------+-----+|
+---------------------+---------------------+
each=: &.> An adverb
(<|. &. > b),(<|. each b) Reversal under open
+---------------------+---------------------+
|+-----+-------+-----+|+-----+-------+-----+|
||3 2 1|7 5 3 2|edcba|||3 2 1|7 5 3 2|edcba||
|+-----+-------+-----+|+-----+-------+-----+|
+---------------------+---------------------+
In mathematics, certain cases of under are called
dual or, dual with respect to:f=: +. &. -. Dual with respect to boolean negation f/~ d=: 0 1 0 0 0 1 D=: &. -. The adverb dual with respect to negation (+.D/~d);(*./~d);(=D/~d);(~:/~d) +---+---+---+---+ |0 0|0 0|0 1|0 1| |0 1|0 1|1 0|1 0| +---+---+---+---+ DWL=: &.^. Dual with respect to natural logarithm DAN=: &. - Dual with respect to arithmetic negation (3 + DWL 4),(3*4),(3 <. DAN 4) , (3 >. 4) 12 12 4 4