A bunch of tautologies about dyadic functions (and about dualities): *. = +.&.-. +. = *.&.-. * = + &.^. % = - &.^. + = * &.^ - = % &.^ <. = >.&.- >. = <.&.-
----- Original Message ----- From: Roger Hui <[email protected]> Date: Sunday, February 1, 2009 21:12 Subject: Re: [Jprogramming] Examples of dyadic forks To: Programming forum <[email protected]> > Depending on the definition of "nontrivial", 3 more examples: > > range=: >. - <. > 5 range 8 > 3 > 5 range _8.2 > 13.2 > > equal=: >. = <. > 3 equal 4 > 0 > 3 equal _5.1 3 400.5 > 0 1 0 > > sgn=: > - < > 3 sgn 4 > _1 > 3 sgn 3 > 0 > 3 sgn _2 > 1 > > x sgn y is _1, 0, or 1, depending on whether x is less than, > equal to, or greater than y. The monad * on real arguments > is sgn&0 . > > > > ----- Original Message ----- > From: Roger Hui <[email protected]> > Date: Sunday, February 1, 2009 19:39 > Subject: Re: [Jprogramming] Examples of dyadic forks > To: Programming forum <[email protected]> > > > The following expresses the tautology that > > ((x^2)-y^2) = (x+y)*(x-y) : > > > > diffsq=: -&*: = + * - > > x=: 0.001 * _1e9 + 10 ?...@$ 2e9 > > y=: 0.001 * _1e9 + 10 ?...@$ 2e9 > > x diffsq y > > 1 1 1 1 1 1 1 1 1 1 > > > > Your question brings to mind events in the early days of J. > > For a time Ken wondered, are there many examples of fork? > > After a while, it seemed that _everything_ was a fork. > > http://keiapl.org/rhui/remember.htm#fork3 > > > > > > > > ----- Original Message ----- > > From: John Randall <[email protected]> > > Date: Sunday, February 1, 2009 15:21 > > Subject: [Jprogramming] Examples of dyadic forks > > To: JProgramming <[email protected]> > > > > > Does anyone have a good example of a dyadic fork? By this > > > I mean one > > > of the form fgh where f and g both use x and y, there are no > [ > > > or ], > > > no constant functions, and no @ or @: . I am having > > > trouble coming up > > > with nontrivial examples. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
