Thank you for the derivatives and integrals. > In particular, if anyone can shed light on the intended use > of 8&o. and _8&o. I would appreciate it.
See Paul Penfield's APL81 paper, "Principal values and branch cuts in complex APL", http://portal.acm.org/citation.cfm?id=805368 the section entitled "New Pythagorean Functions" on page 254. ----- Original Message ----- From: John Randall <[email protected]> Date: Sunday, February 20, 2011 8:25 Subject: Re: [Jprogramming] Derivatives of o. family To: Programming forum <[email protected]> > Here are my suggestions for the result of f d. _1 where f is in the > o. family. > > All of these have been tested by differentiation and comparison with > the original function on suitable arguments. For example > > >./|(((* _1&o.) + 0&o.) D. 1 - _1&o.)"0 ]_1+2*50 > ?@$ 0 > 1.5497e_7 > > is pretty good evidence that (* _1&o.) + 0&o. is an > antiderivative of > _1&o. > > "OK" means that J already knows the integral: "no integral" means > that there isn't one. > > f f d. _1 > 0&o. -:@((* 0&o.) + _1&o.) > 1&o. OK > 2&o. OK > 3&o. OK > 4&o. -:@((* 4&o.)+^.@(+ 4&o.)) > 5&o. OK > 6&o. OK > 7&o. OK > 8&o. j.@-:@((* 4&o.)+^.@(+ 4&o.)) > 9&o. no integral > 10&o. no integral > 11&o. no integral > 12&o. no integral > _1&o. (* _1&o.) + 0&o. > _2&o. (* _2&o.) - 0&o. > _3&o. (* _3&o.) - -:@^.@(1+*:) > _4&o. -:@((* _4&o.) - ^.@(+ _4&o.)) > _5&o. (* _5&o.) - 4&o. > _6&o. (* _6&o.) - _4&o. > _7&o. (* _7&o.) + ^.@(0&o.) > _8&o. -@j.@-:@((* 4&o.)+^.@(+ 4&o.)) > _9&o. -:@*: > _10&o. no integral > _11&o. j.@-:@*: > _12&o. -@j.@(_12&o.) > > Obviously these can be expressed in several ways. Any > improvements would be > welcomed. In particular, if anyone can shed light on the > intended use > of 8&o. and _8&o. I would appreciate it. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
