Re: 4th degree polynomials
- Subject: [mg2196] Re: [mg2119] 4th degree polynomials
- From: Ralheid at aol.com
- Date: Fri, 13 Oct 1995 06:25:34 GMT
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
- Sender: daemon at wri.com ( )
Dear Mr. Moderator That's funny, The question he asked seems perfectly explicit to me. If M is a 4x4 Matrix of what ever symbology the command EigenValues can be used to find its characteristic values. "out = Eigenvalues[m]" in(1)= m2 = {{a,b},{e,f}} out(1)= {{a, b}, {e, f}} in(2)= Timing[Eigenvalues[m2]] 2 2 a + f + Sqrt[a + 4 b e - 2 a f + f ] out(2)= {0.383333 Second, {-------------------------------------, 2 2 2 a + f - Sqrt[a + 4 b e - 2 a f + f ] -------------------------------------}} 2 in(3)= m3 = {{a,b,c},{e,f,g},{i,j,k}} out)3)= {{a, b, c}, {e, f, g}, {i, j, k}} in(4)= Timing[Eigenvalues[m3]]] out(4)= {16.8833333333333333*Second, {-(-a - f - k)/3 - (2^(1/3)* (-a^2 - 3*b*e + a*f - f^2 - 3*c*i - 3*g*j + a*k + f*k - k^2))/ (3*(2*a^3 + 9*a*b*e - 3*a^2*f + 9*b*e*f - 3*a*f^2 + 2*f^3 + 9*a*c*i - 18*c*f*i + 27*b*g*i + 27*c*e*j - 18*a*g*j + 9*f*g*j - 3*a^2*k - 18*b*e*k + 12*a*f*k - 3*f^2*k + 9*c*i*k + 9*g*j*k - 3*a*k^2 - 3*f*k^2 + 2*k^3 + 3^(3/2)*(-(a^2*b^2*e^2) - 4*b^3*e^3 + etc + 30 screens in(5)= Timing[Eigenvalues[m4]] out(5)= Along time but it works Regards Bob Alheid