Re: coefficients of polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg107968] Re: [mg107939] coefficients of polynomial
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Thu, 4 Mar 2010 05:27:29 -0500 (EST)
- References: <201003031052.FAA20347@smc.vnet.net>
Jim Armstrong 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
SolveAlways can be used to solve for some of those coefficients in terms
of others. Then you can use these solutions to rearrange so that you get
solutions for the ones you want (d,e,f in this case).
eqn = a*x^2+b*x*y+c*y^2==d*(x+y)^2+e*(x-y)^2+f*(x^2-y^2);
vars = {a,b,c,d,e,f};
eqns = Thread[vars == (vars /. First[SolveAlways[eqn, {x,y}]])];
In[10]:= InputForm[Solve[eqns, {d,e,f}]]
Out[10]//InputForm= {{d -> (a + b + c)/4, e -> (a - b + c)/4,
f -> (a - c)/2}}
Daniel Lichtblau
Wolfram Research
- References:
- coefficients of polynomial
- From: Jim Armstrong <yusufenginn@yahoo.com>
- coefficients of polynomial