Re: coefficients of polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg107960] Re: coefficients of polynomial
- From: "Nasser M. Abbasi" <nma at 12000.org>
- Date: Thu, 4 Mar 2010 05:26:00 -0500 (EST)
- References: <hmlf1q$jsd$1@smc.vnet.net>
"Jim Armstrong" <yusufenginn at yahoo.com> wrote in message news:hmlf1q$jsd$1 at smc.vnet.net... > 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 > Do you have to automate this? unless you are writing a program, sometimes it is easier just to type a command and copy its output from the screen and use it. So, here I collected terms in xy, then in x^2, then in y^2, and made up 3 equations and solved for d,e,f. expr = a*x^2 + b*x*y + c*y^2 == d*(x + y)^2 + e*(x - y)^2 + f*(x^2 - y^2) Collect[expr, y*x]; eq1 = b == 2*d - 2*e; Collect[expr, x^2]; eq2 = a == d + e + f; Collect[expr, y^2]; eq3 = c == -f; Solve[{eq1, eq2, eq3}, {d, e, f}] Out[42]= a*x^2 + b*x*y + c*y^2 == d*x^2 + e*x^2 + f*x^2 + 2*d*x*y - 2*e*x*y + d*y^2 + e*y^2 - f*y^2 Out[49]= {{d -> (1/4)*(2*a + b + 2*c), e -> (1/4)*(2*a - b + 2*c), f -> -c}} Ofcourse this can be automated using Cases and patterns and such. But again, sometimes for a quick solution, one can just read the output of the last command and use it. ps. I am getting slightly different result than what you have expected. --Nasser