@Carl Love 

Thanks for your reply. But why I can't copy and paste it in another 3D plot? Would you please have a look at the attached file?

Many thanks

MaplePrimes.mw

@acer 

I don't prefer a trigonometric result, unless it's the only possible answer 

@acer 

sorry, what do you mean by "trig calls"?

@Christian Wolinski 

Hi! May I ask how you reached these expressions?

Thanks

@acer 

Yeah, but I mean a simple form. Not such a very complicated one! May I simplify your answer?

@Carl Love 

Hi and thanks.

Then why I don't obtain the forth root using:

evalf(RootOf(6*_Z^3+(27+3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2))*_Z^2+(3*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)*l^4*RootOf(_Z^2*l^2+3*_Z^4-3)^2-9*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)*l^2+45*RootOf(_Z^2*l^2+3*_Z^4-3)^2*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)+90*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2-18*l^4-81+6*l^6*RootOf(_Z^2*l^2+3*_Z^4-3)^2)*_Z-324+108*RootOf(_Z^2*l^2+3*_Z^4-3)^2*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)-63*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)*l^2+30*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)*l^4*RootOf(_Z^2*l^2+3*_Z^4-3)^2-3*sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)*l^6+sqrt(9-3*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2)*l^8*RootOf(_Z^2*l^2+3*_Z^4-3)^2-3*l^8+l^10*RootOf(_Z^2*l^2+3*_Z^4-3)^2+45*l^6*RootOf(_Z^2*l^2+3*_Z^4-3)^2+351*RootOf(_Z^2*l^2+3*_Z^4-3)^2*l^2-108*l^4, index = 4)); 

?

Maple gives an error: " Error, (in RootOf) index should be a positive integer less than 4 "

Thank you

@acer 

Thanks for your reply

Would you want to show me that I can not obtain an explicit answer for rootof in terms of "l"? (Albeit in a more simple form than what you worte). Because you have chosen "l=2", to obtain a solution.

Thanks

@Kitonum 

Dear Kitonum

Thanks for your reply. But my problem is not as easy as what you said. When you use "explicit", you will obtain 11 answers instead of my 7 answers. Actually, I need the eigenvalues related to the eighth case in your answers, and not the seventh.

And also I will be appereciate if you can explain a little about the role of explicit.

Thanks 

@acer 

Dear acer

Here is my program. See ev7, please.

Thanks

MaplePrimesacer.mw

@Kitonum 

Again this is me! I understood that the first line of your answer is the roots of " 

RootOf(_Z^2*l^2+3*_Z^4-3)

"

and the problem of the presence of "l" in your reply has been solved for me. But how about my second question? Why are there 4 roots for a third order equation?

Also, I need the roots of "A", in terms of "l", without indentifying the value of "l". Like the roots of 

RootOf(_Z^2*l^2+3*_Z^4-3)

that you have written in your reply. 

Thank you very much

@Kitonum 

Thanks for your reply. But I think I'm a little confused. You said I need to specify the value of "l", to obtain an explicit form for the rootof. I see that you have chosen "l=1". But I see "l", in your answers yet! Why?

Also, with attention to your reply, I think since my equation is of order 3, so I will find 3 roots, while I see more than 3 roots in your answer. Why?

Thanks a lot

@acer 

Exactly! Thank you very much!

Regards

@Rouben Rostamian

Dear Rouben

Thanks for your nice reply. But I couldn't use your approach in my case, because  it's not a simple field plot. Would you please see the attachment and guide me to find the answer.

Thanks a lotmapleprimes.mw

@Carl Love 

Dear Carl

Thanks for your nice answer

@Carl Love Your assumptions are very interesting to me, because our model parameters have some constraints, physically. These constraints are exactly as your assumptions. A>0 and 0<f<1. Can I ask how did you obtain your result?