Re: Mathematica: Long divison for polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg83809] Re: Mathematica: Long divison for polynomials
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sat, 1 Dec 2007 05:41:51 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <fiopuv$ae7$1@smc.vnet.net>
Caren Balea wrote:
<snip>
> g(x)/h(x) can be also written as
> g(x)/h(x) = 1 - a1*x + (a1^2 - a2)*x^2 + ...
>
> How do I obtain the last expression?
> Which command do I need to use?
It looks like you are talking about power series expansion, am I right?
In this case, just use the built-in function *Series* and possibly
*Normal* if you want to manipulate k(x) as a polynomial. For instance,
In[1]:= g[x_] := 1
h[x_] := 1 + a1*x + a2*x^2 + a3*x^3 + a4*x^4
In[3]:= Series[g[x]/h[x], {x, 0, 2}]
Out[3]= (SeriesData[$CellContext`x, 0, {
1, -$CellContext`a1, $CellContext`a1^2 - $CellContext`a2}, 0, 3, 1])
(* The above line looks better within the FrontEnd ! *)
In[4]:= k[x_] = Normal@Series[g[x]/h[x], {x, 0, 2}]
Out[4]= 1 - a1 x + (a1^2 - a2) x^2
In[5]:= k[2]
Out[5]= 1 - 2 a1 + 4 (a1^2 - a2)
Regards,
--
Jean-Marc