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MathGroup Archive 2007

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Re: Interpreting the solutions... better this time

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75293] Re: Interpreting the solutions... better this time
  • From: "Apostolos E. A. S. Evangelopoulos" <a.e.a.evangelopoulos at sms.ed.ac.uk>
  • Date: Tue, 24 Apr 2007 03:23:50 -0400 (EDT)

Hi, and thanks for getting back to me!

There is one weird thing happening still and that's the following:

If I do substitute for the rest of the variables (R, \[CapitalKappa], \[Gamma] and S) and 'Solve' again for h, the results are:
__________________________________________________________
Solve::verif:Potential solution {h->350.00000000000000000000000000} (possibly discarded by verifier) should be checked by hand. May require use of limits. More...

{{h -> -137.36461551092893 - 286.9990869440407*I}, 
  {h -> -137.36461551092893 + 286.9990869440407*I}, {h -> 96.81264436966121}, 
  {h -> 122.50996762267947 - 157.73801406035219*I}, 
  {h -> 122.50996762267947 + 157.73801406035219*I}, 
  {h -> 442.5965908768586 - 912.0944370543081*I}, 
  {h -> 442.5965908768586 + 912.0944370543081*I}}
__________________________________________________________

1) Back substituting 350 gives 2 infinities, indeed -so we don't care about that.

2) There are left 1 real and 6 complex solutions, adding up to 7 in total. This in NOT in agreement with the previous results of solving the same polynomial, yet symbolically, giving some 17 solutions!! (7 sounds more reasonable for this polynomial, since the highest term is in the 7/3th power)

What do you reckon about this difference in the number of solutions AND
since the numerical solutions above seem to be approximate, is it fine that they've been given directly in this step of solving the equation, without the need of further plugging them into some N[ ] to get the actual values?

Thanks again!


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