[Jprogramming] Cool roots

[Roger Hui]

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 <HenryHRich at nc.rr.com> 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 <km at math.uh.edu> 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 <rogerhui.canada at gmail.com>
>>> wrote:
>>>
>>>  Example from the Iverson and McDonnell *Phrasal
>>>> Forms*<http://www.jsoftware.**com/papers/fork.htm<http://www.jsoftware.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 <km at math.uh.edu> 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
>>>>>
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>