Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

How to find the real and imaginary roots for a complex polynomial?

Status
Not open for further replies.

rahul.6sept

Full Member level 5
Joined
Nov 17, 2006
Messages
242
Helped
1
Reputation
2
Reaction score
1
Trophy points
1,298
Location
Guwahati, India
Activity points
2,884
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.


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

 
Last edited by a moderator:

KlausST

Super Moderator
Staff member
Joined
Apr 17, 2014
Messages
22,994
Helped
4,714
Reputation
9,444
Reaction score
5,079
Trophy points
1,393
Activity points
152,351
Hi,

No test conditions,
No results
No error description..

I can't imagine how someone can help.

Klaus
 

rahul.6sept

Full Member level 5
Joined
Nov 17, 2006
Messages
242
Helped
1
Reputation
2
Reaction score
1
Trophy points
1,298
Location
Guwahati, India
Activity points
2,884
Errors as shown are:

(1) Syntax::tsntxi: "<<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);" is incomplete; more input is needed.

(2) Syntax::sntxi: Incomplete expression; more input is needed .
 

wwfeldman

Advanced Member level 4
Joined
Jan 25, 2019
Messages
1,057
Helped
222
Reputation
443
Reaction score
282
Trophy points
83
Activity points
8,049
would you please write your polynomial on paper and post that?

lines 12 and 13 show up differently - it looks like you missed a space, so it isn't recognizing the format as in a few earlier lines and in line 14.
1 + 4 I space between 4 and I
1 + 6 I space between 6 and I
...
1 + 10I no space between 10 and I

Mathematica is an excellent system
but the user interface does not point out syntax errors
 
Last edited:

Status
Not open for further replies.

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top