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These are replies submitted by goli

@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



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


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

@Christian Wolinski 

Hi! May I ask how you reached these expressions?



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


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.



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.



Dear acer

Here is my program. See ev7, please.




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



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 


that you have written in your reply. 

Thank you very much


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


Exactly! Thank you very much!


@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?

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