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I have the following functions

u2 = 2^(2/3) (12 g1^2 + 12 g2^2 + 12 g3^2 - 4 p^2 + 6 p (κ1 + κ2) - 3 (κ1^2 + κ1 κ2 + κ2^2))/.{g3 -> g1/g2*κ2/2};
u1 = 36 g1^2 (2 p - 3 κ2) - 36 g2^2 (4 p - 3 (κ1 + κ2)) + (2 p - 3 κ1) (36 g3^2 - (2 p - 3 κ2) (4 p - 3 (κ1 + κ2)));

I wish to solve for

g2/.(Solve[u1^2 + u2^3 == 0,g2]/.{Γ -> 20, κ1 -> 1, κ2 -> 2})

and I was returned with several solutions. However, all of the solutions have Root and #. Suggesting that they are of higher ordered radicals. I need to inspect the expressions fully. How should I go about removing the Root and #?

kowalski
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  • Why do you need to convert Root objects to radicals? Is there some code you have that doesn't work with Root objects, so you need radicals? Or, do you just feel more comfortable with radicals? – Carl Woll May 23 '19 at 20:27
  • @CarlWoll I am trying to investigate u1^2+u2^3 = 0 as a function of g1 and g2. Now I'm trying to simplify the expression by giving \[CapitalGamma], \[Kappa]1 and \[Kappa]2 so that I can see the g1 and g2 dependence clearer. You can remove {Γ -> 20, κ1 -> 1, κ2 -> 2} and you will still see Root

    Point is, I'm more comfortable viewing the expression as a whole. Even when it's ugly.

     – kowalski May 23 '19 at 20:39
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    My recommendation is to try to get comfortable working with Root objects, as they are simpler and more robust. – Carl Woll May 23 '19 at 20:48
  • @CarlWoll I doubt that since the expressions are physics related and I will need to examine the expressions in detail to figure out what's going on. But thanks for your help. – kowalski May 23 '19 at 21:01
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    The equation is a $6$th degree polynomial in $\sqrt{g2}$ equal to $0$. Only rarely are $6$th degree polynomial roots expressible in radicals. – Somos May 24 '19 at 00:25

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