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