Polynomial GCD as Linear Combination
- To: mathgroup at smc.vnet.net
- Subject: [mg38319] Polynomial GCD as Linear Combination
- From: "flip" <flip_alpha at safebunch.com>
- Date: Thu, 12 Dec 2002 01:33:10 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello, Can Mathematica do the following? (I provided answers that I did by hand). 1. Find the GCD of f[x_] := x^5 + 4x^4 + 6x^3 + 6x^2 + 5x +2, g[x_] := x^4 + 3x^2 + 3x +6 Answer: gcd (f(x), g(x)) = x^3 + 4x^2 + 5x + 2 over the field Z7? (I think the answer is easy and is yes). 2. Write the GCD above as a linear combination of the given polynomials? Answer: 5*(x^5 + 4x^4 + 6x^3 + 6x^2 + 5x +2) + (2x + 1)*(x^4 + 3x^2 + 3x +6) This one I am not sure about (I guess we can do it piece-meal, but is there a slick function to do it?). Thank you, Flip Please remove "_alpha" to send me email.