> Since abs(4*z^3+4*c*z) is purely real and %e^%i has a nonzero imaginary
> part,
> I think the solution set is empty.
Great . I think that you are right. ( my mistake ). I have made bad
equation.
The initial condition is :
abs(4*z^3+4*c*z)=1
so it should be :
4*z^3+4*c*z=%e^%i
( replacing 1 by %e^%i is special case , I know it)
So I try :
algsys([z=z4+2*c*z2+c2+c, (4*z3+4*c*z)=%e^%i], [c]);
(%o3) []
(%i4) algsys([z=z4+2*c*z2+c2+c, (4*z3+4*c*z)=%e^%i], [c,z]);
(%o4)
[[c=-(sqrt(z4^2+2*c2*z4+(-8*z2-4)*z3+2*%e^%i*z2+c2^2+%e^%i)+z4+c2)/(4*z2+2),z=((8*z2+4)*z3-2*%e^%i*z2-%e^%i)/(2*sqrt(z4^2+2*c2*z4-8*z2*z3-4*z3+2*%e^%i*z2+c2^2+%e^%i)+2*z4+2*c2)
],[c=(sqrt(z4^2+2*c2*z4+(-8*z2-4)*z3+2*%e^%i*z2+c2^2+%e^%i)-z4-c2)/(4*z2+2),z=((8*z2+4)*z3-2*%e^%i*z2-%e^%i)/(-2*sqrt(z4^2+2*c2*z4-8*z2*z3-4*z3+2*%e^%i*z2+c2^2+%e^%i)+2*z4+2*c2)]]
I have tried diffrent value :
(%i5) algsys([z=z4+2*c*z2+c2+c, (4*z3+4*c*z)=1], [c]);
(%o5) []
So still I cant find numerical value of c
Regards
Adam
If I'm wrong about that or if there is a
> typo, maybe we can try solving it with to_poly_solve; something like:
>
> (%i10) eqs : [z=z^4+2*c*z^2+c^2+c, abs(4*z^3+4*c*z)=b]$
> (%i11) assume(b > 0)$
>
> (%i12) to_poly_solve(eqs,[z,c]);
> (%o12) [[z=-sqrt(b)/2,c=-(b^(3/2)+2*b)/(4*sqrt(b))], ... ]
>
> Barton
>
> -----maxima-bounces at math.utexas.edu wrote: -----
>
>
>> 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.