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
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