It would be great for you to fix the addon. We need to work out a way to
authorize you to do so; watch for announcements about this.
It is possible to have d. and D. call an addon, but I don't see that
that makes it much better. And, primitives should only be functions
that have a cast-iron spec. If you even hope to add features to
calculus, it shouldn't be a primitive IMO.
Your proposed enhancements sound good to me. Making such work possible
was why we moved the code into an addon. I hope that users of the
package can come together to agree on improvements.
Henry Rich
On 12/25/2021 10:09 AM, Jan-Pieter Jacobs wrote:
Hi, talking about math/calculus, I'd like to propose something:
The implementation of the fold family (F. &co) has shown that primitives
can be implemented in a J addon (dev/fold).
In view of the recent re-introduction of the modifier trains for backwards
compatibility with reference texts, I think it would make sense to do the
same with d. and D. and, when implemented, Taylor series (i.e. have them
implemented in math/calculus, and use the primitives d. and D. as cover
names).
Recently, I've been going through the math/calculus code, and I'm intending
to try and implement the Taylor series and propose some
improvements/extensions.
So, for the moment I'd like to know: what's the recommended way to
contribute to this addon? I found one small bug in that the derivative of
-. is defined as _1:0, which should have been _1"0 (in primderiv).
What concerns extensions, I had these ideas:
0) Extending to derivatives to non-differentiable functions
I think we could implement many derivatives of discontinuous functions as
"best efforts", e.g. m&>. (which has notable use as 0&>. as ReLU in machine
learning), where we could ignore the non-derivability in a single point, by
fixing a sensible value, in line with 0%0. There's others like | or <. or
. that could be treated similarly.
What are your opinions on this: is this behaviour useful? Should the
resulting function be modified to throw errors in non-differentiable
points? Or perhaps a warning could be given about which points would be
non-differentiable (likely more tricky, because it would require
backtracking through the function to see which values would end up being
not differentiable).
1) Another idea would be trying to simplify the verbs resulting from deriv.
For instance, the 4th derivative of 1&o. should be 1&o. but is currently:
d4 =: 1&o. deriv_jcalculus_ 4
d4
(-@(1&o.) * _1"0@(1&o.))+2&o. * 2&o. * 0"0@(1&o.)
(1&o. -: d4) i: 10
1
However, implementing this generally (i.e. not only for 1&o., or the o.
family) will take implementing half a computer algebra system, which is
well beyond my skill and free time, but could be extremely useful,
especially for applications in e.g. machine learning (see e.g.
https://arxiv.org/abs/1502.05767). Most "competitors" of J also have one,
e.g. Matlab's symbolic toolbox and Python's sympy.
Given J's aptness for concisely expressing mathematical ideas on
"arbitrarily" high dimensional arrays would make J a killer language for
machine learning (and even more if it were easy to use parallel computing
and/or GPU computing, but that's another story, I guess).
Sorry I got into quite a ramble, however, what better to do on Christmas
day.
Merry Christmas to all (or whatever other winter tradition your cultures
might have)!
Jan-Pieter
On Sat, Dec 25, 2021, 02:55 P Padilcdx <[email protected]> wrote:
Thank you for explaining the rationale. Makes sense.
On Dec 24, 2021, at 1:43 PM, Henry Rich <[email protected]> wrote:
They were a dead end. We started a foray into symbolic mathematics and
then realized that J is a much better than C for implementing it in. So we
moved the calculus functions to a J addon, where interested users can make
improvments if they like.
Henry Rich
On 12/24/2021 4:37 PM, P Padilcdx wrote:
Can I ask why they were removed? (Sorry I try to search the forums but
couldn't come up with anything.) Seems like very useful primitives to me
and they are still listed in NuVoc. Hopefully I’m not re-starting a war…
Thanks.
On Dec 24, 2021, at 2:53 AM, Ian Clark <[email protected]> wrote:
withdrawal of d. and D.
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
--
This email has been checked for viruses by AVG.
https://www.avg.com
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
--
This email has been checked for viruses by AVG.
https://www.avg.com
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
