[Maxima] solution of system of quadratic eqns.

[Barton Willis]

> For the more general problem, below, solve() actually executes for a
> very long time before coming back with a  null solution, using your
> current definition of ebaksubst :

The algorithm used by algys just isn't up to this task; the only workaround I know is to use the grobner package.
The optional package to_poly_solve provides a  convenient way to call grobner:

   (%i21) sol : to_poly_solve([(x-a)^2 + (y-b)^2 = r1^2,(x-c)^2 + (y-d)^2 = r2^2], [x,y], 'use_grobner = true)$

Specialize:

   (%i22) subst([a=0,b=0, c=1/2,d=1/2,r1=1,r2=1], sol);
   (%o22) %union([x=1/4-sqrt(7)/4,y=sqrt(7)/4+1/4],[x=sqrt(7)/4+1/4,y=1/4-sqrt(7)/4])

Specialize--oops, not OK for all values of the parameters:

  (%i23) subst([a=0,b=0, c=0,d=0,r1=1,r2=1], sol);
  expt: undefined: 0 to a negative exponent.

For to_poly_solve to autoload like this, you'll need Maxima 2.27, I think