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MathGroup Archive 2007

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Mathematica: Long divison for polynomials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83772] Mathematica: Long divison for polynomials
  • From: Caren Balea <caren_balea at xemail.de>
  • Date: Fri, 30 Nov 2007 05:18:39 -0500 (EST)

Dear all,

I would like to perform long division for a polynomial
using Mathematica.
I came across the command "PolynomialQuotient".

If I consider a function
f(x) = g(x)/h(x)
where degree g(x) > h(x) then I can use PolynomialQuotient
to do the job - no problem.

Now, say, I have
f(x) = 1/h(x)
where
h(x) = 1 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4
and I want to do long division for f(x).

So, I enter

g[x_] := 1
h[x_] := 1 + a1*x + a2*x^2 + a3*x^3 + a4*x^4
k[x_] = PolynomialQuotient[g[x], h[x], x]

and obtain
0.

Which is correct - *but*
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?

Thank you,
Caren


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