Hi,
Thanks for all answers.
I have removed one error in my equation ,
upgraded maxima to last version,
used topoly_solver
and here it is
============= code ===============
load(topoly_solver)$
eq1:z=z^4+2*c*z^2+c^2+c$
eq2:(4*z^3+4*c*z)=1$
to_poly_solve([eq1, eq2], [z, c]);
(%o28) [[z=1/2,c=1/4],[z=-1/2,c=-3/4]]
========================================
It seems good,
second pont c :
c=-3/4
it is a point of internal angle 0 lying on border of hyperbolic
component of period 2
see image :
http://commons.wikimedia.org/w/index.php?title=Image:Mcenter10.jpg
first point c=1/4 is point of internal angle lying on border of
hyperbolic component of period 1
( If I'm not wrong here are solutions for period 2 and its divisors )
For angle 180 [deg]=pi [rad] :
========== code =============
eq1:z=z^4+2*c*z^2+c^2+c$
eq2:(4*z^3+4*c*z)=%e^(%i*%pi)$
to_poly_solve([eq1, eq2], [z, c]);
(%o32)
[[z=%i/2,c=(2*%i+1)/4],[z=-%i/2,c=-(2*%i-1)/4],[z=(sqrt(2)-1)/2,c=-5/4],[z=-(sqrt(2)+1)/2,c=-5/4]]
=============================================
c=-5/4 is good.
First point c=(2*%i+1)/4 is not as I expected ( I expected c=-3/4 )
I don't know why
And now I can solve in general case:
(%i5) eq1:z=z^4+2*c*z^2+c^2+c$
eq2:(4*z^3+4*c*z)=%e^t$
to_poly_solve([eq1, eq2], [z, c]);
(%o7)
[[z=%e^(t/2)/2,c=-(%e^t-2*%e^(t/2))/4],[z=-%e^(t/2)/2,c=-(%e^t+2*%e^(t/2))/4],
[z=(sqrt(1-%e^t)-1)/2,c=(%e^t-4)/4],[z=-(sqrt(1-%e^t)+1)/2,c=(%e^t-4)/4]]
Regards
Adam
Adam Majewski pisze:
> I'm trying to solve system of equations for c:
>
> z=z^4+2*c*z^2+c^2+c
> abs(4*z^3+4*c*z)=%e^%i
>
> It should have 1 complex solution.
>
>
> I have tried :
>
> algsys([z=z^4+2*c*z^2+c^2+c, abs(4*z^3+4*c*z)=%e^%i], [c]);
>
> gives no solutions.
>
> Is it possible in Maxima ?
>
> Adam