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Help with Root function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79407] Help with Root function
  • From: jeremito <jeremit0 at gmail.com>
  • Date: Thu, 26 Jul 2007 05:28:38 -0400 (EDT)

I am trying to find the eigenvalues of a 3x3 matrix with non-numeric
elements.  This requires finding the roots of cubic polynomials.
Mathematica can do this, but I know how to interpret its output.  For
example

In[1]:= B = {{a, 1, 1}, {1, b, 1}, {1, 1, c}}

Out[1]= {{a, 1, 1}, {1, b, 1}, {1, 1, c}}

In[2]:= Eigenvalues[B]

Out[2]= {Root[-2 + a + b + c -
    a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
  1], Root[-2 + a + b + c -
    a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
  2], Root[-2 + a + b + c -
    a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
  3]}


How can I get Mathematica to give me the full answer?  I know it is
long and ugly, but at least I can do something with it.  I can't do
anything with what it gives me now.  Does that make sense?
Thanks,
Jeremy



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