> ... 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.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 <[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/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
