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After using Solve I am choosing the physical root of my equation and dealing further with this root. However, when I am changing parameters using Manipulate, I clearly see not smooth behaviour. Is there a way to cure it? I think, there should be a way of controlling the branch of the square root by adding $\pm i0$.

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    $\begingroup$ I ran into similar issues; basically, you have two choices: 1. Compute the various cases by hand, and hard-program the correct values using Piecewise, or 2. Insert I*e into the square-root expression appropriately, and take the Limit as e->0. Mathematica will give a complicated answer but should result in correctly chosen branches. $\endgroup$
    – QuantumDot
    Commented Aug 8, 2014 at 7:25
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    $\begingroup$ Set Quartics->False so you get solutions as explicit Root[...] objects. Now have your code check for crossings and switch solutions as needed. This can be done by computing parameter values for which there are multiple roots (via a Discriminant computation, say). $\endgroup$ Commented Aug 8, 2014 at 15:31
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    $\begingroup$ I recommend that you include code for an example in your question. $\endgroup$
    – Mr.Wizard
    Commented Aug 14, 2014 at 16:57
  • $\begingroup$ I recommend to examine this answer Finding parameters making real part of eigenvalues vanish especially see the edit. In other words I recommend applying ToRadicals rather than working with simple Root objects. $\endgroup$
    – Artes
    Commented Aug 14, 2014 at 19:31

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