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

```

• Prev by Date: Re: MMA movie with sound to QT
• Next by Date: Re: Help on mathieu equation needed
• Previous by thread: 4th degree polynomials
• Next by thread: Re: 4th degree polynomials