system of equations



-----maxima-bounces at math.utexas.edu wrote: -----

>eq1:z=z^4+2*c*z^2+c^2+c$
>eq2:abs(4*z^3+4*c*z)=1$
>to_poly_solve([eq1, eq2], [z, c]);
>(%o10)
[[z=1/2,c=1/4],[z=-%i/2,c=-(2*%i-1)/4],[z=%i/2,c=-(-2*%i-1)/4],[z=-1/2,c=-
>3/4],[z=-(sqrt(2)+1)/2,c=-5/4],[z=(sqrt(2)-1)/2,c=-5/4]]

I don't know about these equations, but in general to_poly_solve can miss
some
complex solutions; simple example:

 (%i2) to_poly_solve(abs(x)=1,x);
 (%o2) [[x=1],[x=-1]]

The only workaround I know:

 (%i3) to_poly_solve(abs(x+%i*y)=1,[x,y]);
 (%o3) [[x=%r2,y=sqrt(1-%r2^2)],[x=%r1,y=-sqrt(1-%r1^2)]]

Thanks for the interesting problem. Fixing this will be fun, maybe :)

Barton
(author of to_poly & to_poly_solve)