[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>
On 2/20/08, Mark D. Niemiec <mniemiec@interserv.com> wrote:
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
However, "under" can hardly be employed as verb or noun in conventional discourse. Maybe "underate G by F", "underation of G by F"? Subjugate, subjugation? Mmm ... WFL
* Mark D. Niemiec <mniemiec@interserv.com> [Feb 21. 2008 14:56]:
[...]
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
That gives my /etc/sendmail.cf a whole new meaning!
On Fri, 22 Feb 2008, Joerg Arndt wrote:
* Mark D. Niemiec <mniemiec@interserv.com> [Feb 21. 2008 14:56]:
[...]
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
That gives my /etc/sendmail.cf a whole new meaning!
I can't resist the chance to share my tangentially related joke: They say that sendmail was originally thought to be killing an ant with a sledgehammer, but the ant turned out to be an elephant on the horizon.
From which I conclude that using sendmail is like trying to kill an elephant with a sledgehammer.
participants (4)
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Fred lunnon -
Jason -
Joerg Arndt -
Mark D. Niemiec