There was a mistake in taskfmt, but cyclotomic 6 was correct.
cyclotomicREB=:{{{."1 [0.01 round +. p. 1;^j.+:pi* y%~ >:I.1=y +. >:i.y}}
taskfmt=:{{rplc&'_-' rplc&('^1)';')';'x^0';'1') '
'-.~}:,|.')+',~"1'(',"1('1'-.~"1 ":,.0-.~y),"1 'x^',"1":,.I.|y}}
(cyclotomic"0 -: cyclotomicREB"0) >:i.30
1
R.E. Boss
-----Original Message-----
From: Programming <programming-boun...@forums.jsoftware.com> On Behalf Of Raul
Miller
Sent: maandag 21 februari 2022 16:54
To: Programming forum <programm...@jsoftware.com>
Subject: Re: [Jprogramming] polynomial division
That was the first thing I tried.
cyclotomic 6 should return 1 _1 1
Thanks,
--
Raul
On Mon, Feb 21, 2022 at 8:55 AM R.E. Boss <r.e.b...@outlook.com> wrote:
>
> From the hip.
>
> cyclotomic=:{{{."1 [0.01 round +. p. 1;^j.+:pi* y%~ >:I.1=y +. >:i.y}}
> taskfmt=:{{rplc&'_-' rplc&('^1';'';'x^0';'1') '
> '-.~}:,|.')+',~"1'(',"1('1'-.~"1 ":,.0-.~y),"1 'x^',"1":,.I.|y}}
> ([: taskfmt cyclotomic)"0 >:i.30
> (x)+(-1)
> (x)+(1)
> (x^2)+(x)+(1)
> (x^2)+(1)
> (x^4)+(x^3)+(x^2)+(x)+(1)
> (x^2)+(-x)+(1)
> (x^6)+(x^5)+(x^4)+(x^3)+(x^2)+(x)+(1)
> (x^4)+(1)
> (x^6)+(x^3)+(1)
> (x^4)+(-x^3)+(x^2)+(-x)+(1)
> (x0)+(x^9)+(x^8)+(x^7)+(x^6)+(x^5)+(x^4)+(x^3)+(x^2)+(x)+(1)
> (x^4)+(-x^2)+(1)
> (x2)+(x1)+(x0)+(x^9)+(x^8)+(x^7)+(x^6)+(x^5)+(x^4)+(x^3)+(x^2)+(x)+(1)
> (x^6)+(-x^5)+(x^4)+(-x^3)+(x^2)+(-x)+(1)
> (x^8)+(-x^7)+(x^5)+(-x^4)+(x^3)+(-x)+(1)
> (x^8)+(1)
> (x6)+(x5)+(x4)+(x3)+(x2)+(x1)+(x0)+(x^9)+(x^8)+(x^7)+(x^6)+(x^5)+(x^4)
> +(x^3)+(x^2)+(x)+(1)
> (x^6)+(-x^3)+(1)
> (x8)+(x7)+(x6)+(x5)+(x4)+(x3)+(x2)+(x1)+(x0)+(x^9)+(x^8)+(x^7)+(x^6)+(
> x^5)+(x^4)+(x^3)+(x^2)+(x)+(1)
> (x^8)+(-x^6)+(x^4)+(-x^2)+(1)
> (x2)+(-x1)+(x^9)+(-x^8)+(x^6)+(-x^4)+(x^3)+(-x)+(1)
> (x0)+(-x^9)+(x^8)+(-x^7)+(x^6)+(-x^5)+(x^4)+(-x^3)+(x^2)+(-x)+(1)
> (x^22)+(x^21)+(x^20)+(x9)+(x8)+(x7)+(x6)+(x5)+(x4)+(x3)+(x2)+(x1)+(x0)
> +(x^9)+(x^8)+(x^7)+(x^6)+(x^5)+(x^4)+(x^3)+(x^2)+(x)+(1)
> (x^8)+(-x^4)+(1)
> (x^20)+(x5)+(x0)+(x^5)+(1)
> (x2)+(-x1)+(x0)+(-x^9)+(x^8)+(-x^7)+(x^6)+(-x^5)+(x^4)+(-x^3)+(x^2)+(-
> x)+(1)
> (x8)+(x^9)+(1)
> (x2)+(-x0)+(x^8)+(-x^6)+(x^4)+(-x^2)+(1)
> (x^28)+(x^27)+(x^26)+(x^25)+(x^24)+(x^23)+(x^22)+(x^21)+(x^20)+(x9)+(x
> 8)+(x7)+(x6)+(x5)+(x4)+(x3)+(x2)+(x1)+(x0)+(x^9)+(x^8)+(x^7)+(x^6)+(x^
> 5)+(x^4)+(x^3)+(x^2)+(x)+(1)
> (x^8)+(x^7)+(-x^5)+(-x^4)+(-x^3)+(x)+(1)
>
>
> R.E. Boss
>
> -----Original Message-----
> From: Programming <programming-boun...@forums.jsoftware.com> On Behalf
> Of Raul Miller
> Sent: zondag 20 februari 2022 17:35
> To: Programming forum <programm...@jsoftware.com>
> Subject: Re: [Jprogramming] polynomial division
>
> For what it's worth, here's what I was focusing on:
>
> http://rosettacode.org/wiki/Cyclotomic_polynomial#J
>
> As you can see, I altered your polynomial division algorithm -- there's
> enough zeros in the polynomials I was working with, there, that iterating
> through them seemed unwise.
>
> If there's any other significant improvements that you notice -- or any
> errors which I overlooked, of course, please let me know!
>
> Thanks,
>
> --
> Raul
>
> On Sun, Feb 20, 2022 at 11:27 AM 'Michael Day' via Programming
> <programm...@jsoftware.com> wrote:
> >
> > I wrote binc as a monad, just as a quick way of conjuring up sets
> > of binomial coefficients:
> >
> > binc 5
> > 1 5 10 10 5 1
> >
> > 3 binc 5 NB. does work, but not as intended!
> > 1 3 3 1 0 0
> > NB. as does its commute:
> > 5 binc 3
> > 1 5 10 10
> > ... but again, not as I intended.
> >
> > div is what does the division; div&binc a,b just does (binc a) div
> > binc b
> >
> >
> > I wasn't particularly interested in the performance of binc, as Raul
> > was seeking a division algortithm, and binc was just easier than
> > typing 1 5 10 10 5 1 or whatever.
> >
> > I do agree that your definition improves on mine when it matters, eg
> > ts'binc 500x'
> > 0.0392271 460640
> > ts'1, */\ 500x (- % >:@]) i.500x' NB. x=y for my examples
> > 0.001463 504032
> >
> > I suppose it's now worth investigating the performance of div cf
> > dbho and divlo cf dblo excluding the overhead of binc:
> >
> > 'a b' =: binc 50 20
> > a (dbho-:div) b
> > 1
> > ts'a div b'
> > 1.21e_5 5952
> > ts'a dbho b'
> > 2.63e_5 6496
> > a (dblo-:divlo) b
> > 1
> > ts'a divlo b'
> > 1.06e_5 6976
> > ts'a dblo b'
> > 1.75e_5 6496
> >
> > Thanks for pointing out the overheads imposed by binc,
> >
> > Mike
> >
> > On 20/02/2022 16:01, Hauke Rehr wrote:
> > > On my machine, I get
> > >
> > > 100 timespacex '1000x binc 500x'
> > > 0.101916 957376
> > > 100 timespacex '1, */\ 1000x (- % >:@]) i.500x'
> > > 0.00247977 680320
> > >
> > >
> > > Am 20.02.22 um 13:30 schrieb 'Michael Day' via Programming:
> > >> ts'1000x div&binc 500x'
> > >> 2.1598005 4815264
> > >
> >
> >
> > --
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> > https://www.avast.com/antivirus
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