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. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
