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MathGroup Archive 1995

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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


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