I have attached a j script which will provide the same results in Jjhs as
those shown below. In the years I have used APL and J, I have focused on
the use of the notation as a natural way of thinking about mathematical
concepts. Couple this with the executable results of the thinking. To me,
this is the most vital aspect of the notation. If, in the long run it
produces better programmers, that is a bonus.
So, I would appreciate any improvements that could be made in the first
response I have planned as a response to Challenge 8, the creation of a
Shamrock.
In this, I focus on the aspect of mathematics that applies to graphs. Every
point within the equation of a circle satisfies this equation. (This mixes
a little conventional notation and some J for "less than or equal or to"
the radius squared.)
2 2 2
X + y <: r
Using explicit definitions are the best way I know to produce results that
emphasize this concept. However, seeing the tacit expressions (which appear
to be working as I intended them to work) are a way to lead students to a
more sophisticated way to use J as a programmer.
NB. ic is mask for inside the circle
NB. sy is conversion to symbols
NB. gf expands symbols for grapefruit tree
NB. exdwl David Ward Lambert expands symbols with special code
]y=:_5+i.11
_5 _4 _3 _2 _1 0 1 2 3 4 5
ic=: 13 :'(>./y)>:%:(y^2)+/y^2'
ic
>./ >: [: %: (2 ^~ ]) +/ 2 ^~ ]
ic y
0 0 0 0 0 1 0 0 0 0 0
0 0 1 1 1 1 1 1 1 0 0
0 1 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 1 1 0
1 1 1 1 1 1 1 1 1 1 1
0 1 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 1 1 0
0 0 1 1 1 1 1 1 1 0 0
0 0 0 0 0 1 0 0 0 0 0
sy=: 13 : '((ic y)+(ic y)*?1+10*ic y) {x'
NB. For some reason I can't replace 10 with _2+$c
sy
[ {~ ([: ic ]) + ([: ic ]) * [: ? 1 + 10 * [: ic ]
c=:' ||\\//OOOOO'
$c
12
c sy y
|
/|\|OO|
|/OOOOO\O
O/OO|O/|\
|O|O\\|O\
O|/O/|/OO\|
/\O/|\OO\
O/|OOOO/O
OO\|\\O/\
|\O\/O\
|
gf=: 13 :'|.,"2 |:(x sy y),:"2'' '''
gf
[: |. [: ,"2 [: |: ' ' ,:"2~ sy
c gf y
O
O O \ / \ / \
| O \ \ O O O O O
O O O O O \ O / O
| O O O \ \ | O O
\ O / O O / O O O O O
\ O / \ O | / O /
O O O O O O O O O
O / \ \ O \ O O O
\ \ O O \ | |
\
exdwl=: 13 :'1j1&#"1 x sy y'
exdwl
[: 1j1&#"1 sy
c exdwl y
O
O O / | / O O
\ \ | \ O O \ | O
/ O O / / / O O \
\ O / / O | / O O
| | / \ / \ O / O / O
\ \ \ | O O O | \
/ \ O O \ | \ O \
O O O O O O | O /
\ O \ | / / /
O
This is a "grapefruit tree" seen from an airplane. David Ward Lambert
provided his improvement to the final function which will be a challenge for
programmers.
Since there are some who would discourage the use of 13 : I would
appreciate a way that is as transparent as this for mathematics educators
(one of the groups Ken Iverson sought to attract).
Please give some thought to students in early stages of Algebra, and find a
way to give them a real feeling for the equation of a "painted circle" on
the Cartesian plane. I'd enjoy seeing better alternatives.
Linda
-----Original Message-----
From: programming-boun...@jsoftware.com
[mailto:programming-boun...@jsoftware.com] On Behalf Of Raul Miller
Sent: Monday, March 19, 2012 4:11 PM
To: Programming forum
Subject: Re: [Jprogramming] why=: 13 :'y*y*y'
For what it's worth, J's problem with 13 :'y+y' is probably something like:
original y+y
made tacit +~
simplified +
In other words, since + is commutative, the ~ is "unnecessary".
Except, of course, that's only relevant for expressions like 13 :'x+y'
So, anyways, I expect that the problem is that the rule that supports
simplification for commutative expressions has lost the context that would
be necessary to know that it's applicable.
If I am right, the simple solution would be to remove that simplification
when the arguments are not available (which might be always).
--
Raul
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