# Root: Simplifying symbolic expression

I'm doing calculations with a lot of symbols, which don't always gives nice expressions. Now I have a solution with a Root-expression, where the coefficients are symbolic, e.g.

Root[Z + Y#1 + X#1^2 - Conjugate[Y]#1^3 + Conjugate[Z]#1^4,1]


Is there a way to simplify this with Mathematica? How would you treat these kind of expressions?

• Are y and z complex or real-valued? – 2012rcampion Apr 24 '15 at 14:01
• Your Root object is missing the &. If you use ToRadicals you can convert the Root object to the equivalent algebraic expression which is much more complicated. Adding any appropriate assumptions to Simplify may help but the Root object is probably the simplest form. Read the documentation for examples on how to use the Root objects. – Bob Hanlon Apr 24 '15 at 14:05
• @2012rcampion every variable is complex valued... – cherzieandkressy Apr 24 '15 at 18:14
• @BobHanlon OK, I hoped there was a simpler way, but thanks! – cherzieandkressy Apr 24 '15 at 18:14

Solve[Z + Y #1 + X #1^2 - Conjugate[Y] #1^3 + Conjugate[Z] #1^4 &[x] == 0, x, Quartics -> True]

• Ok, I didn't realise this. It's just that I want to understand the output from for example Integrate[-((2 I \[Pi])/Sqrt[(r + A xiR - rb xiR^2)^2 - 4 (l xiR + w xiR^2 + Z) (wb - lb xiR + xiR^2 Zb)]),xiR] which gives an EllipticF[ArcSin[...]] from a gigantic expressions with a lot of Roots... I want to find the an expression for A wherefore this integral becomes zero but it's too complicated to understand so I wanted to simplify this integral... – cherzieandkressy Apr 28 '15 at 10:34