That's exactly right. You will have a conjunction that creates a verb.
Remains to be decided what you should do if you can't symbolically
integrate u.
Since your d. replacement would have to handle differentiation too, it
would emit a verb to do secant approximation if it couldn't symbolically
differentiate u.
Henry Rich
On 10/1/2017 9:30 PM, 'Jon Hough' via Source wrote:
Seems like an interesting project. My initial thoughts are how to parse the
verbs.
I suppose f` ''
essentially gives the representation of the verb, which can be tokenized and
then symbolically evaluated.
e.g.
f=:%+*:
g=. (f f.)`''
Then tokenize g into the consituent verbs, and evaluate from there.
Am I going in the wrong direction? This is just an initial thought.
--------------------------------------------
On Fri, 9/29/17, Henry Rich <henryhr...@gmail.com> wrote:
Subject: Re: [Jsource] Low hanging fruit in d.
To: sou...@jsoftware.com
Date: Friday, September 29, 2017, 12:45 PM
IIRC Roger decided that
implementing d. in C code was a mistake, because
there are so many possible forms. They could
be recognized by a J
adverb that analyzed
the operand and produced the correct verb. Then it
would be easy to expand the list.
So we haven't worked much
on fixing/extending d.
The
real boon would be if you stepped up and wrote that adverb
(in J)
that did the work of d. . I will
help you if you like. The end result
would be better symbolic integration.
If you make progress, we could
think about how to make a J primitive
(d.)
turn into an invocation of a user-defined verb: a feature
that
would have wide ramifications.
Henry Rich
On 9/28/2017 11:38 PM, 'Jon Hough' via
Source wrote:
> Looking through cd.c
(bearing in mind I am still trying to get my head around the
source code), I noticed d. has missed a lot of low hanging
fruit in the form of
>
> (f * g) d. _1
>
> e.g from around line 337 of cd.c:
> static F2(jtintgtymes){A f=a,g=w;
> RZ(a&&w);
> R A0;
> } /*
integral of a * w */
>
> d. gives up for pretty much any case of f
* g, when it should be possible to evaluate a lot of
expressions, e.g. polynomial * exponential and some trig *
exponential, and some trig * polynomial.
>
> I know symbolic
integration is a vipers nest and the complexity can
explode, but it should be possible to add more functionality
to d.
>
> I have done
some playing around and implemented some functionality (poly
* exp), but still very messy and not worth showing yet. One
issue is tidying up the resulting expression. e.g.
rebracketing and factoring out common expressions.
>
> Anyway, I wonder if
it is worth adding more functionality to d.
>
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