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Re: determining coefficients of a polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124382] Re: determining coefficients of a polynomial
  • From: janos <janostothmeister at gmail.com>
  • Date: Wed, 18 Jan 2012 05:56:22 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jf3cda$nj3$1@smc.vnet.net>

On Jan 17, 9:44 am, klw1026 <klw1... at gmail.com> wrote:
> Hi,
>
> Here's my problem: I have two rational polynomials in two variables, say x and y, with one having arbitrary coefficients. I would like to compare these two polys and solve for the arbitrary coefficients. For example, suppose the polys are $f(x,y) = \frac{2}{xy} - xy + \frac{x}{y} + \frac{y}{x}$ and $g(x,y) = \cdot\cdot\cdot + n_1\frac{1}{xy} + n_2 xy + n_3\frac{x}{y}+ n_4\frac{y}{x} +\cdot\cdot\cdot$. Then you can see that $n_1 = 2$, $n_2=-1$, $n_3 = n_4 =1$ and all other $n_i = 0$. Does anyone know how to do this with Mathematica?
>
> Thanks

One solution might be:
SolveAlways[f[x, y] - g[x, y] == 0, {x, y}]
giving
{{n1 -> 2, n2 -> -1, n3 -> 1, n4 -> 1}}

I hope this helps.

J=E1nos



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