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Re: polynomial division

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42007] Re: polynomial division
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 16 Jun 2003 03:57:40 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <bbmu7c$ju$1@smc.vnet.net> <bbq6eu$csv$1@smc.vnet.net> <bc6ngj$2gt$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <bc6ngj$2gt$1 at smc.vnet.net>,
 Marian Otremba <marianUSUN at zeus.polsl.gliwice.pl> wrote:

>  OK if x<<1   
> 
> for example
> n=6;
> p= x^2+x+1;
> w1=Series[1/p,{x,0,n}] // Normal
> Plot[1/p-w1,{x,0,1/2},PlotRange->All]

Or, generally,

   n=6;

   p[x_] = 1/(x^2+x+1);

   q[x_,x0_:0] := Normal[p[x] + O[x,x0]^n]

and for x << 1,

   q[x]

   Plot[p[x] - %, {x,0,1/2}, PlotRange->All];

> if x >>1
> 
> w2=(Series[(1/p) /. x->1/u,{u,0,n}]//Normal) /. u->1/x
> Plot[1/p-w2,{x,2,5},PlotRange->All]

For x >> 1, then

   q[x,Infinity]

   Plot[p[x] - %, {x,2,5}, PlotRange->All];

> if x about 1 
> 
> w3=((Series[(1/p) /. x->1/(u+1),{u,0,n}]//Normal) /. u->1/x-1)//Expand
> Plot[1/p-w3,{x,2/3,2},PlotRange->All]

and for x ~ 1,
  
   q[x,1]

   Plot[p[x] - %, {x,2/3,2}, PlotRange->All];

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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