Yes, I've just checked m14 - it rather looks as if I was plagiarising it!
It uses 0: , ] rather than my 0&, ...
I haven't ever checked whether using a verb constant like 0: is
"better" than the noun 0 . Early versions of J didn't permit
constants in forks, so 0 , ] wasn't allowed.
FWIW, if you want to represent root(s(s-a)(s-b)(s-c)) more directly,
here's another line by line development. Indented lines are my
input, the left-adjusted lines are the interpreter's result.
s =: -:@:(+/) NB. semiperimeterverb
s 3 4 5 NB. semiperimeter of a,b,c
6
(s - ])3 4 5 NB. s - (a, b, c)
3 2 1
(s( */@: - )])3 4 5 NB. (s-a)(s-b)(s-c)
6
(s([ * */@: - )])3 4 5 NB. s(s-a)(s-b)(s-c)
36
(s([ %:@* */@: - )])3 4 5 NB. Root[s(s-a)(s-b)(s-c)]
6
(s([ %:@* */@: - )]) NB. Tacit expression
s ([ %:@* */@:-) ]
(s([ %:@* */@: - )]) f. NB. Expanded form
-:@:(+/) ([ %:@* */@:-) ]
As I hope you can see, s is evaluated just the once, and then applied
as the left hand argument with a,b,c as the right hand argument.
Cheers,
Mike
On 04/09/2018 23:11, Martin Kreuzer wrote:
@Mike
Yes, it does help, as
it is a sort of eye-opener, rephrasing the fourth factor (s) as (s-0),
and
it answers my (yet un-uttered) question about "m14".
-M
At 2018-09-04 13:46, 'Mike Day' via Programming wrote:
Does this help?
Each line is a small amendment to the preceding one...
(-:@(+/))3 4 5 NB. Semiperimeter, s
(-:@(+/)-0&,)3 4 5 NB. s - 0, a, b, c
6 3 2 1
(-:@(+/)*/@:-0&,)3 4 5 NB. s * (s - a) * ...
36
(-:@(+/)%:@(*/)@:-0&,)3 4 5 NB. Heronâs formula applied to 3 4 5
(-:@(+/)%:@(*/)@:-0&,) NB. Let interpreter remove unnecessary
brackets...
-:@(+/) %:@(*/)@:- 0&,
So the semiperimeter is calculated just the once. It relies on
converting the triplet a,b,c to the quadruplet 0, a, b, c, rather
than doing particularly smart bracketing.
I donât often use [: but if you prefer it, the following arises
from a similar building process using [: rather than @ and @:
([:-:(+/))3 4 5
(([:-:(+/)) - 0&,)3 4 5
6 3 2 1
(([:-:(+/))( [: */ - )0&,)3 4 5
36
(([:-:(+/))( [: %: [: */ - )0&,)3 4 5
(([:-:(+/))( [: %: [: */ - )0&,) NB. Get rid of extra brackets
([: -: +/) ([: %: [: */ -) 0&,
Cheers,
Mike
Sent from my iPad
> On 4 Sep 2018, at 12:50, Martin Kreuzer <i...@airkreuzer.com> wrote:
>
> Hi all -
>
> To calculate the area of a flat triangle, using Heron's formula,
> A(a,b,c)= sqrt( s2*(s2-a)*(s2-b)*(s2-c) )
> I wrote a simple function doing this:
>
> * get the three sides (as list input y)
> * compute the half perimeter s2
> * build the differences s2-y
> * build product
> * take square root
>
> My explicit solution looks like this
>
> taher=: 13 : '%: s2 * */ s2-y [ s2=. -: +/ y'
>
> and works
>
> taher 3 4 5
> 6
>
> Suggested tacit version looks like this (and works too)
>
> tahert=: [: %: ([: -: +/) * [: */ ([: -: +/) - ]
>
> Q: Is there a way to reference the intermediate result of ([: -:
+/) the half perimeter s2
> within the tacit expression, as has been done in the explicit..?
> [Guess the interpreter takes care of this anyway; my question aims
at whether a shorter formulation could be reached.]
>
> Thanks
> -M
>
> ----------------------------------------------------------------------
> 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 Avast antivirus software.
https://www.avast.com/antivirus
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
