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Re: Re: coefficients of polynomial

• To: mathgroup at smc.vnet.net
• Subject: [mg108013] Re: [mg107975] Re: [mg107939] coefficients of polynomial
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 5 Mar 2010 04:33:00 -0500 (EST)
• References: <201003031052.FAA20347@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

That doesn't work:

Block[{equ =
    a x^2 + b x y + c y^2 == d (x + y)^2 + e (x - y)^2 + f (x^2 - y^2),
    con = MonomialList[equ[[1]] - equ[[2]], {x, y}] /. x | y -> 1},
  Solve[Thread[con == 0], {d, e, f}]]

{{d -> -((e (x - y)^2)/(x + y)^2) - (f (x - y))/(
     x + y) - (-a x^2 - b x y - c y^2)/(x + y)^2}}

But this does:

Block[{equ =
    a x^2 + b x y + c y^2 == d (x + y)^2 + e (x - y)^2 + f (x^2 - y^2),
    con},
  con = MonomialList[equ[[1]] - equ[[2]], {x, y}] /. x | y -> 1;
  Solve[Thread[con == 0], {d, e, f}]]

{{d -> 1/4 (a + b + c), e -> 1/4 (a - b + c), f -> (a - c)/2}}

Bobby

On Thu, 04 Mar 2010 04:28:46 -0600, Christoph Lhotka <lhochr at gmail.com>  
wrote:

> hi, try out
>
> Block[
>  {equ = a x^2 + b x y + c y^2 == d (x + y)^2 + e (x - y)^2 + f (x^2 -  
> y^2),
>    con = MonomialList[equ[[1]] - equ[[2]], {x, y}] /. x | y -> 1},
>  Solve[Thread[con == 0], {d, e, f}]
>  ]
>
> Christoph
>
>
> 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
>>
>>
>>
>>
>
>


-- 
DrMajorBob at yahoo.com

• References:
  • coefficients of polynomial
    • From: Jim Armstrong <yusufenginn@yahoo.com>