Thanks Raul and Don, Here are some NaN meaNderings:
[L=:(-_),(-2%~1-~%:5),0,(2%~1-~%:5),_
__ _0.618034 0 0.618034 _
%/~L
|NaN error: scriptd
| %/~L
|[-2] c:\users\user\j804-user\temp\25.ijs
L%/L
|NaN error: scriptd
| L %/L
|[-4] c:\users\user\j804-user\temp\25.ijs
L%/}.}:L
_ __ __
1 __ _1
0 0 0
_1 _ 1
__ _ _
(}.}:L)%/L
0 1 __ _1 0
0 0 0 0 0
0 _1 _ 1 0
(}.}:L)%table L
----------T--------------------------┐
│% │__ _0.618034 0 0.618034 _│
+---------+--------------------------+
│_0.618034│ 0 1 __ _1 0│
│ 0│ 0 0 0 0 0│
│ 0.618034│ 0 _1 _ 1 0│
L---------+---------------------------
L%/table }.}:L
----------T---------------------┐
│%/ │_0.618034 0 0.618034│
+---------+---------------------+
│ __│ _ __ __│
│_0.618034│ 1 __ _1│
│ 0│ 0 0 0│
│ 0.618034│ _1 _ 1│
│ _│ __ _ _│
L---------+----------------------
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Linda A
Alvord
Sent: Monday, November 16, 2015 9:31 AM
To: [email protected]
Subject: Re: [Jprogramming] Why is subtraction and division of rational
numbers so hard?
Don, Can you identify which ones of the twenty five items in the pairs don't
work?
%/~ 1r3%i.5
|NaN error
| %/~1r3%i.5
Linda
-----Original Message-----
From: <mailto:[email protected]>
[email protected]
[ <mailto:[email protected]>
mailto:[email protected]] On Behalf Of Don Kelly
Sent: Monday, November 16, 2015 12:59 AM
To: <mailto:[email protected]> [email protected]
Subject: Re: [Jprogramming] Why is subtraction and division of rational
numbers so hard?
Could it be that 1r3 % i.1 =(1/3)%0 so the result of the summation is
infinity + some numbers?
try
-/~ 1r3 %1 +i.5
0 1r6 2r9 1r4 4r15
_1r6 0 1r18 1r12 1r10
_2r9 _1r18 0 1r36 2r45
_1r4 _1r12 _1r36 0 1r60
_4r15 _1r10 _2r45 _1r60 0
or
-/~ 1r3 %1r1000000+i.5
0 1000000000000r3000003 2000000000000r6000003 1000000000000r3000001
4000000000000r12000003
_1000000000000r3000003 0 1000000000000r6000009000003
2000000000000r9000012000003 1000000000000r4000005000001
_2000000000000r6000003 _1000000000000r6000009000003 0
1000000000000r18000015000003 2000000000000r24000018000003
_1000000000000r3000001 _2000000000000r9000012000003
_1000000000000r18000015000003 0 1000000000000r36000021000003
_4000000000000r12000003 _1000000000000r4000005000001
_2000000000000r24000018000003 _1000000000000r36000021000003 0
Don Kelly
On 11/15/2015 1:05 AM, Linda A Alvord wrote:
> How would you explain to a 4th grade student why subtraction and
> division of fraction is so difficult for J. Here is a dialog I wrote
> to review all the big ideas students should remember from third grade.
> Tables show how some verbs like + and times are commutative and * and
> % are not. If the
verb
> is commutative you need only "master" a little more than half of the
table.
>
>
>
>
>
>
>
> +/~i.5
>
>
> i.
> 0 1 2 3 4
>
> 1 2 3 4 5
>
> 2 3 4 5 6
>
> 3 4 5 6 7
>
> 4 5 6 7 8
>
>
>
>
>
>
>
> -/~i.5
>
>
>
> 0 _1 _2 _3 _4
>
> 1 0 _1 _2 _3
>
> 2 1 0 _1 _2
>
> 3 2 1 0 _1
>
> 4 3 2 1 0
>
>
>
>
>
>
>
> */~i.5
>
>
>
> 0 0 0 0 0
>
> 0 1 2 3 4
>
> 0 2 4 6 8
>
> 0 3 6 9 12
>
> 0 4 8 12 16
>
>
>
>
>
>
>
> %/~i.5
>
>
>
> 0 0 0 0 0
>
> _ 1 0.5 0.333333 0.25
>
> _ 2 1 0.666667 0.5
>
> _ 3 1.5 1 0.75
>
> _ 4 2 1.33333 1
>
>
>
>
>
>
>
> 1r3%i.5
>
>
>
> _ 1r3 1r6 1r9 1r12
>
>
>
>
>
>
>
> +/~ 1r3%i.5
>
>
>
> _ _ _ _ _
>
> _ 2r3 1r2 4r9 5r12
>
> _ 1r2 1r3 5r18 1r4
>
> _ 4r9 5r18 2r9 7r36
>
> _ 5r12 1r4 7r36 1r6
>
>
>
>
>
> -/~ 1r3%i.5
>
>
>
> |NaN error
>
> | -/~1r3%i.5
>
>
>
>
>
> */~ 1r3%i.5
>
>
>
> _ _ _ _ _
>
> _ 1r9 1r18 1r27 1r36
>
> _ 1r18 1r36 1r54 1r72
>
> _ 1r27 1r54 1r81 1r108
>
> _ 1r36 1r72 1r108 1r144
>
>
>
>
>
>
>
> %/~ 1r3%i.5
>
>
>
> |NaN error
>
> | %/~1r3%i.5
>
>
>
>
>
>
>
> t=: 13 :'>:/~i.y'
>
>
>
> t 5
>
>
>
> 1 0 0 0 0
>
> 1 1 0 0 0
>
> 1 1 1 0 0
>
> 1 1 1 1 0
>
> 1 1 1 1 1
>
>
>
>
>
>
>
> (t 5)*+/~i.5
>
>
>
> 0 0 0 0 0
>
> 1 2 0 0 0
>
> 2 3 4 0 0
>
> 3 4 5 6 0
>
> 4 5 6 7 8
>
>
>
>
>
>
>
> (t 5)**/~i.5
>
>
>
> 0 0 0 0 0
>
> 0 1 0 0 0
>
> 0 2 4 0 0
>
> 0 3 6 9 0
>
> 0 4 8 12 16
>
>
>
>
>
>
>
> (t 5)*+/~ 1r3%i.5
>
>
>
> _ 0 0 0 0
>
> _ 2r3 0 0 0
>
> _ 1r2 1r3 0 0
>
> _ 4r9 5r18 2r9 0
>
> _ 5r12 1r4 7r36 1r6
>
>
>
>
>
>
>
> (t 5)**/~ 1r3%i.5
>
>
>
> _ 0 0 0 0
>
> _ 1r9 0 0 0
>
> _ 1r18 1r36 0 0
>
> _ 1r27 1r54 1r81 0
>
> _ 1r36 1r72 1r108 1r144
>
>
>
>
>
>
>
> Linda I
>
>
>
>
>
> ----------------------------------------------------------------------
> For information about J forums see <http://www.jsoftware.com/forums.htm>
http://www.jsoftware.com/forums.htm
>
----------------------------------------------------------------------
For information about J forums see <http://www.jsoftware.com/forums.htm>
http://www.jsoftware.com/forums.htm
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http://www.jsoftware.com/forums.htm
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