[arndt@jjj.de: [arndt@jjj.de: Re: wishlist: evaluating polcyclo() and others]]

["Karim Belabas" <Karim.Belabas@math.u-bordeaux1.fr>]

[ Posted on behalf of Joerg, who is being persecuted by qsecretary -- K.B.]

----- Forwarded message from Joerg Arndt <arndt@jjj.de> -----

Date: Fri, 9 Nov 2007 10:48:00 +1100
From: Joerg Arndt <arndt@jjj.de>
To: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Cc: pari-dev <pari-dev@list.cr.yp.to>
Subject: Re: wishlist: evaluating polcyclo() and others


For the Chebyshev polynomials (and all types
of linear recurrences) use the function frec() from:
http://www.jjj.de/pari/fastrec.inc.gp

Both Chebyshev T and U can also be computed via
http://www.jjj.de/pari/cheby.inc.gp
Slightly faster methods are described on 
pp.648-649 of the fxtbook
( http://www.jjj.de/fxt/#fxtbook )

But you are right, saying
  poltcheby(2)
should really not return an error.

Same for polcyclo()

For the latter, there is an algorithm in
  Joachim von zur Gathen, Jürgen Gerhard: "Modern Computer Algebra"
  Cambridge University Press, second edition, 2003.

If this mail does not appear on the list then it is the third
one silently dropped  8-(


* Jeroen Demeyer <jdemeyer@cage.ugent.be> [Nov 09. 2007 10:10]:
> Hello,
> 
> This is a long-time wishlist item of mine.  It concerns the functions 
> which compute certain polynomials, for example polcyclo(), 
> polchebyshev(), pollegendre() and maybe others.  These functions take an 
> argument which is the variable, but I would really like to put anything 
> there, for example polcyclo(10^6, 2) would compute the value of the 
> 10^6-th cyclotomic polynomial at the point 2.  Or polchebyshev(10^4, 
> x*Mod(1,3)) to get the 10^4-th Chebyshev polynomial mod 3.  Essentially 
> polcyclo(n,a) should be the same as subst(polcyclo(n),x,a).
> 
> 
> Cheers,
> Jeroen.

----- End forwarded message -----
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Karim Belabas                  Tel: (+33) (0)5 40 00 26 17
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