Re: 4th degree polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg2196] Re: [mg2119] 4th degree polynomials
- From: Ralheid at aol.com
- Date: Fri, 13 Oct 1995 02:25:34 -0400
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