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Re: coefficients of polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108021] Re: [mg107939] coefficients of polynomial
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Fri, 5 Mar 2010 04:34:29 -0500 (EST)

Try this:

pol1 = a x^2 + b x y + c y^2;
pol2 = d (x + y)^2 + e (x - y)^2 + f (x^2 - y^2) // Expand;
dif = Collect[pol1 - pol2, {x^2, y^2, x y}];
Solve[{Coefficient[dif, x^2] == 0, Coefficient[dif, y^2] == 0, 
  Coefficient[dif, x y] == 0}, {d, e, f}]

Welcome. 


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


-- 
Alexei Boulbitch, Dr., habil.
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