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Regarding solving a polynomial: gives empty output

Hello All,

I am trying to solve the equation given in the notebook attached.
The algebraic expression is not giving the roots. It is showing like, {{}}.
I don't understand what does it mean. Can anyone help me this? How should I solve such an expression?

Attachments:
Untitled-1.nb
POSTED BY: Neetasha Arya
6 Replies
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Ok, try with 3/2+1/5:

In[17]:= 
xxxx /. {me -> 1, Te -> 1, \[Omega]pe -> 1, \[Omega]ce -> 1, 
   ky -> 1, \[Epsilon]b -> 1, c -> 1, k -> 1, kpar -> 1, 
   kz -> 1, \[Omega]pi -> 1, 
   vde -> 1, \[Kappa] -> 3/2 + 1/5, \[Phi] -> Pi/6};
N[%*\[Omega]^2 // Simplify, 10] // Expand

Out[18]= -49.8649146 - 3491.27281 \[Omega] + 9421.90942 \[Omega]^2 + 
 643294.193 \[Omega]^3 - (42938.7191 + 141.5690054 I) \[Omega]^4 + 
 17009.04504 \[Omega]^6
POSTED BY: Gianluca Gorni

Try with kappa=1/7:

xxx /. {me -> 1, Te -> 1, \[Omega]pe -> 1, \[Omega]ce -> 1, 
  ky -> 1, \[Epsilon]b -> 1, c -> 1, k -> 1, kpar -> 1, 
  kz -> 1, \[Omega]pi -> 1, 
  vde -> 1, \[Kappa] -> 1/7, \[Phi] -> Pi/6}
N[%*\[Omega]^2 // Simplify, 10] // Expand
POSTED BY: Gianluca Gorni

There is a limit for [kappa] value, it should be greater than 3/2.
POSTED BY: Neetasha Arya

Even if I put the value of \Kappa = 2 (say), It is showing output as complex infinity.

.

Later If I evaluate it element wise, it is showing complex infinity for 

HypergeometricPFQ[{1/2, 1/2, 1}, {-\[Kappa] , 1, 1, 1}, 
 2*\[Lambda]*\[Kappa]]

and showing some answer for 

HypergeometricPFQ[{1, 1/2, 1}, {-\[Kappa] + 1/2, 1, 1, 1}, 
 2*\[Lambda]*\[Kappa]]

What is the problem ?

Attachments:
hypergeometic.nb
POSTED BY: Neetasha Arya

Your equation is of degree 6 in omega, with very complicated coefficients:

In[318]:= PolynomialQ[Expand[xxx*\[Omega]^2], \[Omega]]
Exponent[Expand[xxx*\[Omega]^2], \[Omega]]

Out[318]= True

Out[319]= 6

It seems hopless, unless you set most parameters to numbers.
POSTED BY: Gianluca Gorni
Eric Rimbey
Eric Rimbey
Posted 3 years ago

The empty lists means that Solve found no solutions. As for how to find solutions, your expressions are way too complicated for me to try to debug your code.
POSTED BY: Eric Rimbey
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