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)+(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^7)+(-x^5)+(-x^4)+(-x^3)+(x)+(1)
R.E. Boss
-----Original Message-----
From: Programming <[email protected]> On Behalf Of Raul
Miller
Sent: zondag 20 februari 2022 17:35
To: Programming forum <[email protected]>
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
<[email protected]> 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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> ----------------------------------------------------------------------
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