On 28.02.2013 19:53, Raymond Toy wrote:
>>>>>> "Adam" == Adam <adammaj1 at o2.pl> writes:
>
> Adam> my errors :
>
> Adam> ====================
> Adam> (%i1) z:x+y*%i;
> Adam> (%o1) %i*y+x
> Adam> (%i2) f:z^4-z;
> Adam> (%o2) (%i*y+x)^4-%i*y-x
> Adam> (%i3) solve(f=z,[x,y]);
> Adam> (%o3)
> Adam> [[x=%r1,y=sqrt(-2*%r1^2-(-6*%r1^2-3*4^(1/3))/3+2^(5/3))/2+%i*%r1+%i/2^(2/3)],[x=%r2,y=-sqrt(-2*%r2^2-(-6*%r2^2-3*4^(1/3))/3+2^(5/3))/2+%i*%r2+%i/2^(2/3)],[x=%r3,y=sqrt(-2*%r3^2-(-6*%r3^2-3*4^(1/3))/3-2^(5/3))/2+%i*%r3-%i/2^(2/3)],[x=%r4,y=-sqrt(-2*%r4^2-(-6*%r4^2-3*4^(1/3))/3-2^(5/3))/2+%i*%r4-%i/2^(2/3)]]
> Adam> (%i4) multiplicities;
> Adam> (%o4) []
>
>
> Hmm. Maybe multiplicities doesn't work for solving for several
> variables. But in this case, why not just do
>
> (%i2) solve(zz^4-zz=zz,zz);
> (%o2) [zz = (2^(1/3)*sqrt(3)*%i-2^(1/3))/2,
> zz = -(2^(1/3)*sqrt(3)*%i+2^(1/3))/2,zz = 2^(1/3),zz = 0]
> (%i3) multiplicities;
> (%o3) [1,1,1,1]
>
> Then you can get the real and imaginary parts separately from these
> solutions.
>
> (%i4) map(lambda([r], [x = realpart(rhs(r)), y = imagpart(rhs(r))]), %o2);
> (%o4) [[x = -1/2^(2/3),y = sqrt(3)/2^(2/3)],
> [x = -1/2^(2/3),y = -sqrt(3)/2^(2/3)],[x = 2^(1/3),y = 0],
> [x = 0,y = 0]]
>
> Ray
>
Thx for all answers.
I have put Maxima code and images here :
http://en.wikibooks.org/wiki/Fractals/Multibrot_sets
Adam