Re: coefficients of polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg107982] Re: [mg107939] coefficients of polynomial
- From: "Tony Harker" <a.harker at ucl.ac.uk>
- Date: Thu, 4 Mar 2010 05:30:04 -0500 (EST)
- References: <201003031052.FAA20347@smc.vnet.net>
One slightly sneaky way is
ll=LogicalExpand[
a x^2 + b x y + c y^2 ==
d (x + y)^2 + e (x - y)^2 + f (x^2 - y^2) + O[y]^3 + O[x]^3]
which returns
-c + d + e - f == 0 && -a + d + e + f == 0 && -b y + 2 d y - 2 e y ==
0
wnd then
Solve[List @@ ll, {d, e, f}]
will give
{{f -> (a - c)/2, d -> 1/4 (a + b + c), e -> 1/4 (a - b + c)}}
Tony Harker
]-> -----Original Message-----
]-> From: Jim Armstrong [mailto:yusufenginn at yahoo.com]
]-> Sent: 03 March 2010 10:52
]-> To: mathgroup at smc.vnet.net
]-> Subject: [mg107939] coefficients of polynomial
]->
]-> 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
]->
]->
- References:
- coefficients of polynomial
- From: Jim Armstrong <yusufenginn@yahoo.com>
- coefficients of polynomial