[math-fun] Re: F^-1(G(F(x)))

On 16 Feb 2008 at 18:58, Steve Witham wrote:

Is there a common name for the idiom F^-1( G( F( x ) ) ) ?

In the J programming language, this is denoted by G &. F and is called "G under F". (J (http://jsoftaware.com) is the descendent of APL, also designed by Kenneth Iverson, and it includes functional programming operators, as well as using ASCII characters for readability.) Under can also be used dyadically: F^-1( G( F(x), F(y)) for example: x +&.*: y NB. Euclidean distance (*: is square) x +&.% y NB. Electrical resistance in parallel (% is reciprocal) x -:@+ y NB. Arithmetic mean (-: is halve; F@G(x,y) = F(G(x,y)) ) x -:@+&.% y NB. Harmonic mean -- Mark D. Niemiec <mniemiec@interserv.com>