How is p. implemented? - Bo
>________________________________ > Fra: Roger Hui <rogerhui.can...@gmail.com> >Til: Programming forum <programm...@jsoftware.com> >Sendt: 9:13 onsdag den 12. december 2012 >Emne: Re: [Jprogramming] Cool roots > >> ... 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 <rogerhui.can...@gmail.com>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 <henryhr...@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 <k...@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.can...@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 <k...@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 >>>>>>> >>>>>>> ------------------------------**------------------------------** >>>>>>> ---------- >>>>>>> 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/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 > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
