Don Guinn wrote:
> Given:
> f =: ^&_0.001
> The integral of f as a J expression ignoring an arbitrary constant is
> if =: _1000*^&_0.001
The primitive conjunction D. is "derivative". So, for example f D.1 is
the first derivative of f, namely _0.001 * ^&( _0.001 - 1) :
^&_0.001 D. 1
(* =/~@(i...@$))@:(_0.001&*@(^&_1.0009999999999999))
I'm not sure why the results are diagonalized with (* =/~@(i...@$)) but
then it's a long time since I took calculus.
Anyway, conceptually, if f D.1 is the first derivative of f then f D._1
is the first integral of f, and if J could symbolically calculate these the way
it symbolically calculates derivatives, then Dieter could have his "right
answer" with:
1 -&(f D. _1) _
or using your insert-style:
-&(f D. _1)/ 1 _
And he could "believe" it more or less blindly (in the same way we "believe"
213213123x * 9918831771x more or less blindly, i.e. believe=trust). But, at
the moment, J does not support integrals (negative RHAs to D. ):
^&_0.001 D. _1
|nonce error
| ^&_0.001 D._1
Since, with positive RHAs, J already identifies and manipulates the relevant
information from a useful subset of LHAs, would be much trouble to support
negative RHAs for this same subset? Or even a smaller subset; I'm thinking
particularly of x&p. D. n for numeric (maybe real?) vector x (and scalar
integer n negative or positive obviously).
-Dan
PS: Never thought of it before, but D.0 is a cute identity adverb in J:
('arbitrary function' [ ;:) D. 0
'arbitrary function' [ ;:
similarly for @.0 (but v...@. is undocumented). Also, I just realized I
can do sneaky tricks with u`v D. n .
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