rahul.6sept
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Hi, I want to find the real and imaginary roots of a complex polynomial. I'm using MATHEMATICA for the same. I'm getting some errors and i'm unable to debug the same.
I want to post it here so that someone can guide me so as to get the roots.
I'm not sure if it is the right platform for Mathematica code related questions, but since I'm doing it for Physics hence I'm putting it here.
I want to post it here so that someone can guide me so as to get the roots.
I'm not sure if it is the right platform for Mathematica code related questions, but since I'm doing it for Physics hence I'm putting it here.
Code dot - [expand] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 *Subscript[\[CapitalOmega], 1][Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]+Subscript[I\[CapitalOmega], i];(Subscript[\[CapitalOmega], 2]^2)[Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]^2 (1+4Subscript[I\[CapitalOmega], i]-2Subscript[I\[CapitalOmega], i] Subscript[\[CapitalOmega], r]-3Subscript[\[CapitalOmega], i]^2+2Subscript[\[CapitalOmega], i]^2 Subscript[\[CapitalOmega], r]);* *(Subscript[\[CapitalOmega], 3]^3)[Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]^3 (1+6Subscript[I\[CapitalOmega], i]-3Subscript[I\[CapitalOmega], i] Subscript[\[CapitalOmega], r]-9Subscript[\[CapitalOmega], i]^2+6Subscript[\[CapitalOmega], i]^2 Subscript[\[CapitalOmega], r]);* *(Subscript[\[CapitalOmega], 4]^4)[Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]^4 (1+8Subscript[I\[CapitalOmega], i]-4Subscript[I\[CapitalOmega], i] Subscript[\[CapitalOmega], r]-18Subscript[\[CapitalOmega], i]^2+12Subscript[\[CapitalOmega], i]^2 Subscript[\[CapitalOmega], r]);* *(Subscript[\[CapitalOmega], 5]^5)[Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]^5 (1+10Subscript[I\[CapitalOmega], i]-5Subscript[I\[CapitalOmega], i] Subscript[\[CapitalOmega], r]-30Subscript[\[CapitalOmega], i]^2+20Subscript[\[CapitalOmega], i]^2 Subscript[\[CapitalOmega], r]);**(Subscript[\[CapitalOmega], 6]^6)[Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]^6 (1+12Subscript[I\[CapitalOmega], i]-6Subscript[I\[CapitalOmega], i] Subscript[\[CapitalOmega], r]-45Subscript[\[CapitalOmega], i]^2+30Subscript[\[CapitalOmega], i]^2 Subscript[\[CapitalOmega], r]);* *(Subscript[\[CapitalOmega], 7]^7)[Subscript[\[CapitalOmega], r]_Integer,Subscript[\[CapitalOmega], i_]Integer]:=Subscript[\[CapitalOmega], r]^7 (1+14Subscript[I\[CapitalOmega], i]-7Subscript[I\[CapitalOmega], i] Subscript[\[CapitalOmega], r]-63Subscript[\[CapitalOmega], i]^2+42Subscript[\[CapitalOmega], i]^2 Subscript[\[CapitalOmega], r]);* *Subscript[P, 1],Subscript[P, 2],Subscript[P, 3],Subscript[P, 4],Subscript[P, 5],Subscript[A, 10],Subscript[R, 0],Subscript[R, 1],Subscript[R, 2],Subscript[R, 3],Subscript[R, 4],Subscript[R, 5],Subscript[R, 1]^',Subscript[R, 2]^',Subscript[R, 3]^',Subscript[R, 4]^',Subscript[R, 0]^',e ,Subscript[\[Omega], J],Subscript[\[Nu], id],Subscript[\[Omega], d],k,\[Xi] and \[CapitalDelta] denotes constant terms * T1:=(Re[z]+I Im[z])/.z->(1+I); T2:=Re[z]^2 (1+4 I Im[z]-2I Im[z]Re[z]-3 Im[z]^2+2 Im[z]^2 Re[z])/.z->(1+I); T3:=Re[z]^3 (1+6 I Im[z]-3I Im[z]Re[z]-9 Im[z]^2+6 Im[z]^2 Re[z])/.z->(1+I); T4:=Re[z]^4 (1+8 I Im[z]-4I Im[z]Re[z]-18 Im[z]^2+12 Im[z]^2 Re[z])/.z->(1+I); T5:=Re[z]^5 (1+10I Im[z]-5I Im[z]Re[z]-30 Im[z]^2+20 Im[z]^2 Re[z])/.z->(1+I); T6:=Re[z]^6 (1+12I Im[z]-6I Im[z]Re[z]-63 Im[z]^2+42 Im[z]^2 Re[z])/.z->(1+I); T7:=Re[z]^7 (1+14 I Im[z]-63 Im[z]^2-7 I Im[z] Re[z]+42 Im[z]^2 Re[z])/.z->(1+I); Reduce[Subscript[P, 1](Subscript[P, 2]((Subscript[P, 5]-Subscript[A, 10])(Subscript[R, 1]T1+Subscript[R, 2]T2+Subscript[R, 3]T3-Subscript[R, 4]T4-Subscript[R, 5]T5+Subscript[R, 0])Subscript[\[Nu], id]+I(Subscript[P, 5]-Subscript[A, 10])(Subscript[R, 1]^' T1+Subscript[R, 2]^' T2+Subscript[R, 3]^' T3-Subscript[R, 4]^' T4+Subscript[R, 0]^')Subscript[\[Nu], id]+(Subscript[R, 1]T2+Subscript[R, 2]T3+Subscript[R, 3]T4-Subscript[R, 4]T5-Subscript[R, 5]T6+Subscript[R, 0]T1)Subscript[\[Nu], id] Subscript[\[Omega], J]/\[Xi]+I(Subscript[R, 1]^' T2+Subscript[R, 2]^' T3+Subscript[R, 3]^' T4-Subscript[R, 4]^' T5+Subscript[R, 0]^' T1)Subscript[\[Nu], id] Subscript[\[Omega], J]/\[Xi]+(Subscript[R, 1]T3+Subscript[R, 2]T4+Subscript[R, 3]T5-Subscript[R, 4]T6-Subscript[R, 5]T7+Subscript[R, 0]T2)Subscript[\[Omega], J] Subscript[\[Omega], d]k+I(Subscript[R, 1]^' T3+Subscript[R, 2]^' T4+Subscript[R, 3]^' T5-Subscript[R, 4]^' T6+Subscript[R, 0]^' T2)Subscript[\[Omega], J] Subscript[\[Omega], d]k+I(Subscript[R, 1]T2+Subscript[R, 2]T3+Subscript[R, 3]T4-Subscript[R, 4]T5-Subscript[R, 5]T6+Subscript[R, 0]T1)Subscript[P, 6]-(Subscript[R, 1]^' T2+Subscript[R, 2]^' T3+Subscript[R, 3]^' T4-Subscript[R, 4]^' T5+Subscript[R, 0]^' T1)Subscript[P, 6]+I(Subscript[R, 1]T3+Subscript[R, 2]T4+Subscript[R, 3]T5-Subscript[R, 4]T6-Subscript[R, 5]T7+Subscript[R, 0]T2)Subscript[\[Omega], J] Subscript[\[Omega], d]/\[Xi]-(Subscript[R, 1]^' T3+Subscript[R, 2]^' T4+Subscript[R, 3]^' T5-Subscript[R, 4]^' T6+Subscript[R, 0]^' T2)Subscript[\[Omega], J] Subscript[\[Omega], d]/\[Xi])+Subscript[P, 3]e((Subscript[R, 1]T3+Subscript[R, 2]T4+Subscript[R, 3]T5-Subscript[R, 4]T6-Subscript[R, 5]T7+Subscript[R, 0]T2)Subscript[\[Omega], J] Subscript[\[Omega], d]+I(Subscript[R, 1]^' T3+Subscript[R, 2]^' T4+Subscript[R, 3]^' T5-Subscript[R, 4]^' T6+Subscript[R, 0]^' T2)Subscript[\[Omega], J] Subscript[\[Omega], d]-I(Subscript[R, 1]T2+Subscript[R, 2]T3+Subscript[R, 3]T4-Subscript[R, 4]T5-Subscript[R, 5]T6+Subscript[R, 0]T1)Subscript[P, 7]+Subscript[P, 7](Subscript[R, 1]^' T2+Subscript[R, 2]^' T3+Subscript[R, 3]^' T4-Subscript[R, 4]^' T5+Subscript[R, 0]^' T1)-Subscript[A, 10](Subscript[R, 1]T1+Subscript[R, 2]T2+Subscript[R, 3]T3-Subscript[R, 4]T4-Subscript[R, 5]T5+Subscript[R, 0])Subscript[\[Nu], id]-I(Subscript[R, 1]^' T1+Subscript[R, 2]^' T2+Subscript[R, 3]^' T3-Subscript[R, 4]^' T4+Subscript[R, 0]^')Subscript[A, 10] Subscript[\[Nu], id])-(e(Subscript[R, 1]T1+Subscript[R, 2]T2+Subscript[R, 3]T3-Subscript[R, 4]T4-Subscript[R, 5]T5+Subscript[R, 0])Subscript[\[Nu], id]+I(Subscript[R, 1]^' T1+Subscript[R, 2]^' T2+Subscript[R, 3]^' T3-Subscript[R, 4]^' T4+Subscript[R, 0]^')Subscript[e\[Nu], id]+I(Subscript[R, 1]T2+Subscript[R, 2]T3+Subscript[R, 3]T4-Subscript[R, 4]T5-Subscript[R, 5]T6+Subscript[R, 0]T1)Subscript[e\[Omega], d]-(Subscript[R, 1]^' T2+Subscript[R, 2]^' T3+Subscript[R, 3]^' T4-Subscript[R, 4]^' T5+Subscript[R, 0]^' T1)Subscript[e\[Omega], d]))(1/\[Xi]^2+k^2)+Subscript[P, 4]((Subscript[R, 1]T1+Subscript[R, 2]T2+Subscript[R, 3]T3-Subscript[R, 4]T4-Subscript[R, 5]T5+Subscript[R, 0])Subscript[\[Nu], id]^2+I(Subscript[R, 1]^' T1+Subscript[R, 2]^' T2+Subscript[R, 3]^' T3-Subscript[R, 4]^' T4+Subscript[R, 0]^')Subscript[\[Nu], id]^2+(Subscript[R, 1]T3+Subscript[R, 2]T4+Subscript[R, 3]T5-Subscript[R, 4]T6-Subscript[R, 5]T7+Subscript[R, 0]T2)Subscript[\[Omega], d]^2+I(Subscript[R, 1]^' T3+Subscript[R, 2]^' T4+Subscript[R, 3]^' T5-Subscript[R, 4]^' T6+Subscript[R, 0]^' T2)Subscript[\[Omega], d]^2)+\[CapitalDelta](Subscript[A, 1] Subscript[B, 3](1/\[Xi]+Ik)Subscript[\[Nu], id]^2+Subscript[T2A, 1] Subscript[B, 3](1/\[Xi]+Ik)Subscript[\[Omega], d]^2+Subscript[T1A, 2] Subscript[A, 7] Subscript[\[Lambda], J](k^2+1/\[Xi]^2)(1/\[Xi]-k)Subscript[\[Omega], J] Subscript[\[Nu], id]^2+Subscript[T3A, 2] Subscript[A, 7] Subscript[\[Lambda], J](k^2+1/\[Xi]^2)(1/\[Xi]-k)Subscript[\[Omega], J] Subscript[\[Omega], d]^2-Subscript[A, 2] Subscript[A, 7] Subscript[\[Lambda], J](k^2+1/\[Xi]^2)(1/\[Xi]-k)Subscript[\[Nu], id]^2-Subscript[T2A, 2] Subscript[A, 7] Subscript[\[Lambda], J](k^2+1/\[Xi]^2)(1/\[Xi]-k)Subscript[\[Omega], d]^2)==0]//Simplify
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