Very nice, thank you.
This took my code from me using jbreak during a division because I was
tired of starting at the hourglass to having that operation complete
nearly instantly.
Thanks again,
--
Raul
On Sun, Feb 20, 2022 at 6:31 AM 'Mike Day' via Programming
<programm...@jsoftware.com> wrote:
>
> This approach, from my A-level Maths perhaps, seems far too simple compared
> to that of the article, but works, on this iPad running J701 (no, it can’t
> run Ian’s J902!), including when dbho or dblo throws a domain error for, eg,
> dividing order 50 by order 30. I haven’t tried in J903 on the laptop yet.
>
> BTW, I couldn’t understand why the article shows a remainder,
> ]q=. e dbho c 1 3 3 1
> ]r=.e-c t q 0 0 0 0 2 3
> But I realised there’s a missing definition, eg E =. 1 5 10 10 7 4, with e
> replaced by E in the next 2 lines.
>
> Anyway,
>
> NB. binomial coefficients for (1+z)^y
> binc =: !~i.@>:
>
> NB. x % y
> div =: 3 : 0 NB. similar result to Ken's dbho
> :
> q =. ''
> yx=. y,:x
> n =. 2 + x -&# y
> while. n =. <: n do.
> q =. q, r =. %~/ {."1 yx
> yx =. y,: }. -~/ yx * r,1
> end.
> q
> )
>
> divlo =: div&.:|. NB. Like Ken's dblo
>
> diva =: 3 : 0 NB. a bit less elegant. Similar performance
> :
> q =. ''
> n =. 2 + x -&# y
> ly=. #y
> while. n =. <: n do.
> q =. q, r =. x %&{. y
> if. |r do.
> d =. (ly{.x) -&}. r * y
> x =. d, ly}.x
> else.
> x =. }. x
> end.
> end.
> q
> )
> 5 div&binc 3
> 1 2 1
> 5 div&binc 2
> 1 3 3 1
>
> ts
> 6!:2 , 7!:2@]
> ts'50 diva&binc 10'
> 0.000554 9216
> ts'50 div&binc 10'
> 0.000661 13824
> ts'50 dbho&binc 10'
> 0.002024 211840
> ts'50 dbho&binc 30'
> |domain error: dbho
> | (d{.x) %.(2#d=.<./$M){.M=.y+/ .*y bq x
>
> I slightly prefer div to diva.
>
> Cheers,
>
> Mike
> Sent from my iPad
>
> > On 20 Feb 2022, at 03:46, Raul Miller <rauldmil...@gmail.com> wrote:
> >
> > https://code.jsoftware.com/wiki/Essays/Polynomial+Division
> >
> > Iverson's method for polynomial division is elegant, but it's a bit
> > slow for large polynomials (order greater than 2000).
> >
> > Does anyone have a more efficient approach? Or is this one of those
> > situations where it doesn't get any better?
> >
> > Thanks,
> >
> > --
> > Raul
> > ----------------------------------------------------------------------
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> ----------------------------------------------------------------------
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