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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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closed as off-topic by Michael E2, MarcoB, dr.blochwave, Mr.Wizard Aug 12 '15 at 23:13

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  • "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – Michael E2, MarcoB, dr.blochwave, Mr.Wizard
If this question can be reworded to fit the rules in the help center, please edit the question.

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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 Aug 8 '14 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). $\endgroup$ – Daniel Lichtblau Aug 8 '14 at 15:31
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    $\begingroup$ I recommend that you include code for an example in your question. $\endgroup$ – Mr.Wizard Aug 14 '14 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 Aug 14 '14 at 19:31

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