It there some way to have these three work the same way in a script. Here's my
jijs:
a=:0 { ]
b=:1 { ]
c=:2 { ]
roots2=:(2*a)%~([:-b)(+,-)[:%:([:*:b)-4*a*c
roots2 1 3 2
_1 _2
roots2 1 1 1
_0.5j0.866025 _0.5j_0.866025
roots2 1 0 _1
1 _1
'a b c'=:1 1 1
rootsHR=:((a %~ ]) , (c % ])) _0.5 * b +`-@.(0>[) %: (*:b) - 4*a*c
rootsHR
_0.5j_0.866025 _0.5j0.866025
erase names 'a b c'
1 1 1
a=:0 { ]
b=:1 { ]
c=:2 { ]
roots2=:(2*a)%~([:-b)(+,-)[:%:([:*:b)-4*a*c
roots2 1 3 2
_1 _2
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of km
Sent: Wednesday, December 12, 2012 11:09 PM
To: [email protected]
Subject: Re: [Jprogramming] Cool roots
Cool!
Sent from my iPad
On Dec 12, 2012, at 6:00 PM, Henry Rich <[email protected]> wrote:
> Oh, I see. the signum function mustn't return 0. Should be
>
> ((a %~ ]) , (c % ])) _0.5 * b +`-@.(0>[) %: (*:b) - 4*a*c
>
>
> Henry Rich
>
> On 12/12/2012 10:30 AM, km wrote:
>> Henry, the combined form below fails when b is 0. Kip
>>
>> r
>> 3 : 0
>> 'a b c' =. y
>> ((a %~ ]) , (c % ])) _0.5 * (%: (*:b) - 4*a*c) ((* *) + ]) b
>> )
>> r 1 3 2
>> _2 _1
>> r 1 2 1
>> _1 _1
>> r 1 0 1
>> 0 _
>> r 1 0 _1
>> 0 __
>> roots 1 0 1
>> 0j1 0j_1
>> roots 1 0 _1
>> 1 _1
>>
>> Sent from my iPad
>>
>>
>> On Dec 12, 2012, at 6:25 AM, Henry Rich <[email protected]> wrote:
>>
>>> I have to disagree. That's way cool.
>>>
>>> I assumed you used Newton's method to shine up the final values of the
>>> roots, but I never knew you tried rational results too.
>>>
>>> It is possible to produce accurate results for quadratics without such
>>> heroic measures. You just can't use the quadratic formula like you learned
>>> it in highschool.
>>>
>>> There's the usual quadratic formula:
>>>
>>> (2*a) %~ (-b) (+,-) %: (b^2) - 4*a*c
>>>
>>> and there's a less-well-known alternative form:
>>>
>>> (2*c) % (-b) (-,+) %: (b^2) - 4*a*c
>>>
>>> Each version produces two roots. The roots created are more accurate when
>>> +-(-b) is positive, so you can get one accurate root from each formula.
>>>
>>> To calculate, use the combined form
>>>
>>> ((a %~ ]) , (c % ])) _0.5 * (%: (*:b) - 4*a*c) ((* *) + ]) b
>>>
>>> Accuracy has a coolness all its own.
>>>
>>> Henry Rich
>>>
>>> On 12/12/2012 3:13 AM, Roger Hui wrote:
>>>>> ... produce more accurate results in some difficult cases.
>>>>
>>>> c=: p. <20$1.5
>>>> c
>>>> 3325.26 _44336.8 280799 _1.1232e6 3.18239e6 _6.78911e6 1.13152e7
>>>> _1.50869e7
>>>> 1.63441e7 _1.45281e7 1.0654e7 _6.45695e6 3.22847e6 _1.3245e6 441501
>>>> _117734
>>>> 24527.8 _3847.5 427.5 _30 1
>>>> p. c
>>>> ┌─┬────────────────────────────────────────────────────────────────
>>>> ───────────────┐
>>>> │1│3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2 3r2
>>>> 3r2 3r2
>>>> 3r2 3r2│
>>>> └─┴────────────────────────────────────────────────────────────────
>>>> ───────────────┘
>>>>
>>>>
>>>>
>>>> On Tue, Dec 11, 2012 at 11:29 PM, Roger Hui
>>>> <[email protected]>wrote:
>>>>
>>>>> You may or may not know that p. employs some extraordinary measures which
>>>>> produce more accurate results in some difficult cases. But those
>>>>> extraordinary measures are not "cool". For example:
>>>>>
>>>>> w=: p. <1+i.20 NB. Wilkinson's
>>>>> polynomial<http://en.wikipedia.org/wiki/Wilkinson_polynomial>
>>>>> w
>>>>> 2432902008176640000 _8752948036761600000 13803759753640704000
>>>>> _12870931245150988800 8037811822645051776 _3599979517947607200
>>>>> 1206647803780373360 _311333643161390640 63030812099294896
>>>>> _10142299865511450 1307535010540395 _135585182899530 11310276995381
>>>>> _7561...
>>>>>
>>>>> p. w
>>>>> ┌─┬──────────────────────────────────────────────────┐
>>>>> │1│20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1│
>>>>> └─┴──────────────────────────────────────────────────┘
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> On Tue, Dec 11, 2012 at 3:40 PM, Henry Rich <[email protected]> wrote:
>>>>>
>>>>>> None of these cute ways is very accurate in tough cases:
>>>>>>
>>>>>> 0j15 ": (2*a) %~ (-b) (+,-) %: (b^2) - 4*a*c [ 'a b c' =. 1e_6
>>>>>> 1e6 1e_6
>>>>>> 0.000000000000000 _1000000000000.000000000000000
>>>>>>
>>>>>> But p. does better:
>>>>>>
>>>>>> 0j15 ": 1 {:: p. c,b,a
>>>>>> _1000000000000.000000000000000 _0.000000000001000
>>>>>>
>>>>>> Henry Rich
>>>>>>
>>>>>>
>>>>>>
>>>>>> On 12/11/2012 6:29 PM, Roger Hui wrote:
>>>>>>
>>>>>>> There are some cheeky (or is it cheesy?) versions:
>>>>>>>
>>>>>>> (2*a) %~ (-b) (+,-) %: (b^2) - 4*a*c NB. Kip Murray
>>>>>>> (2*a) %~ - b (+,-) %: (b^2) - 4*a*c
>>>>>>> (+:a) %~ - b (+,-) %: (*:b) - 4*a*c
>>>>>>> -: a %~ - b (+,-) %: (*:b) - 4*a*c
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Tue, Dec 11, 2012 at 11:37 AM, km <[email protected]> wrote:
>>>>>>>
>>>>>>> It appears this could be translated into J as the rather cool
>>>>>>>>
>>>>>>>> (2*a) %~ (-b) (+,-) %: (b^2) - 4*a*c
>>>>>>>>
>>>>>>>> Sent from my iPad
>>>>>>>>
>>>>>>>>
>>>>>>>> On Dec 11, 2012, at 12:59 PM, Roger Hui
>>>>>>>> <[email protected]>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>> Example from the Iverson and McDonnell *Phrasal
>>>>>>>>> Forms*<http://www.jsoftware.**com/papers/fork.htm<http://www.j
>>>>>>>>> software.com/papers/fork.htm>>paper
>>>>>>>>> (which
>>>>>>>>> introduced fork):
>>>>>>>>>
>>>>>>>>> (-b)(+,-)√((b*2)-4×a×c)÷2×a
>>>>>>>>>
>>>>>>>>> √ is a postulated APL primitive, spelled %: in J.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On Tue, Dec 11, 2012 at 10:49 AM, km <[email protected]> wrote:
>>>>>>>>>
>>>>>>>>> What is the coolest way of programming the quadratic formula
>>>>>>>>> in J? We are
>>>>>>>>
>>>>>>>>> finding the roots of polynomial c + x*(b + x*a) without using
>>>>>>>>> p. . I offer
>>>>>>>>
>>>>>>>>>
>>>>>>>>>> roots
>>>>>>>>>> 3 : 0
>>>>>>>>>> 'a b c' =. y
>>>>>>>>>> q =. %: (b^2) - 4*a*c
>>>>>>>>>> (2*a) %~ (-b) + q,-q
>>>>>>>>>> )
>>>>>>>>>> roots 1 3 2
>>>>>>>>>> _1 _2
>>>>>>>>>> roots 1 0 1
>>>>>>>>>> 0j1 0j_1
>>>>>>>>>> roots 1 _2 1
>>>>>>>>>> 1 1
>>>>>>>>>>
>>>>>>>>>> partly as problem definition. I am looking for cool roots verbs!
>>>>>>>>>>
>>>>>>>>>> Kip Murray
>>>>>>>>>>
>>>>>>>>>> Sent from my iPad
>>>>>>>>>>
>>>>>>>>>> ------------------------------**-----------------------------
>>>>>>>>>> -**
>>>>>>>>>> ----------
>>>>>>>>>> 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>
>>>>>>>> ------------------------------**------------------------------*
>>>>>>>> *
>>>>>>>> ----------
>>>>>>>> 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/f
>>>>>>> orums.htm>
>>>>>>>
>>>>>>>
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>>>>>> rums.htm>
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>> ---------------------------------------------------------------------
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> ----------------------------------------------------------------------
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