Re: coefficients of polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg107991] Re: [mg107939] coefficients of polynomial
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Thu, 4 Mar 2010 05:31:45 -0500 (EST)
- Reply-to: hanlonr at cox.net
eqn = a x^2 + b x y + c y^2 ==
d (x + y)^2 + e (x - y)^2 + f (x^2 - y^2);
soln = Solve[
Thread[
Flatten[
CoefficientList[#, {x, y}]] & /@
eqn],
{d, e, f}][[1]]
{d -> (1/4)*(a + b + c),
e -> (1/4)*(a - b + c), f -> (a - c)/2}
eqn /. soln // Simplify
True
Bob Hanlon
---- Jim Armstrong <yusufenginn at yahoo.com> wrote:
=============
Hi,
I am trying to find the coefficients d,e,f of this simple equating:
ax^2+bxy+cy^2=d(x+y)^2+e(x-y)^2+f(x^2-y^2)
I mean I am waiting for this type of solution:
d=(a-b+c)/2
e=b/2
f=(a-c)/2
so how can I get these constants?
I searched it and tried to use Solve, Expand...but either they dont give it or they solve it in terms of all terms (a,b,c,x,y).
Thanks a lot