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
