Help me solve a symbolic polynomial with complex coefficient

[aibrahim]

Dear All,

I want to solve a symbolic polynomial with complex cofficient and find its roots in terms of symboles

example:

(((s-I*w)^2+g1)*((s-I*w)^2+g2)+(a1+a2*(s-I*w))+(a3+a4*(s-I*w))*((s-I*w)^2+g1))

Where I=√-1 and g1,g2,w,a1,a2,a3,a4 are symboles

and i want to solve this equation in s

i try maple functions but i don't reach roots of the polynomial in terms of this symboles if any can help me through suggesting another function in maple or matlab i will be greatful.

Regards,

 

[saeidj]

Re: symbolic polynomial

Dear friend

You can use MATLAB to solve it:

syms g1 g2 w a1 a2 a3 a4 ;
R = solve('(((s-i*w)^2+g1)*((s-i*w)^2+g2)+(a1+a2*(s-i*w))+(a3+a4*(s-i*w))*((s-i*w)^2+g1))','s')


Regards

 

[aibrahim]

Re: symbolic polynomial

Thanks alot,

I try it but the solution is no longer simplified and i try simplify and pretty function in matlab but still solution not simplified can you suggest me away to get readable form for the solution.

Regards,

 

[saeidj]

Re: symbolic polynomial

Dear friend

You have 7 unknown variables in your equation, so the roots can not have very simple terms.

In this program:
syms g1 g2 w a1 a2 a3 a4 ;
R = solve('(((s-i*w)^2+g1)*((s-i*w)^2+g2)+(a1+a2*(s-i*w))+(a3+a4*(s-i*w))*((s-i*w)^2+g1))','s');

R : ( size= 4x1 and Bytes=2141680).

Using expand function:

K = expand(R);

K : ( size= 4x1 and Bytes=1397784).

I think to simplify more, you should substitute some of unknown variables with known values. For example:

N=subs(K,{a1,a2,a3,a4},{'1', '2', '3', '4'});
L=simplify(N);
H=expand(L);

H : ( size= 4x1 and Bytes=96568).

Best