2 x**2 + 4*y**2 - 4; 2*y**2 - x; TITLE : Mickey-mouse example to illustrate homotopy continuation. ROOT COUNTS : total degree : 4 1-homogeneous Bezout number : 4 with partition : {x y } generalized Bezout number : 4 based on the set structure : {x y }{x y } {x y }{y } mixed volume : 4 REFERENCES : The equations represent the intersection of a circle with a parabola. Jan Verschelde and Ronald Cools: "Polynomial Homotopy Continuation, A Portable Ada Software Package". The Ada-Belgium Newsletter, 4:59--83, 1996. Proceedings of the 1996 Ada-Belgium Seminar, 22 November 1996, Eurocontrol, Brussels, Belgium. THE SOLUTIONS : 4 2 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x : -3.23606797749979E+00 0.00000000000000E+00 y : 0.00000000000000E+00 -1.27201964951407E+00 == err : 1.174E-15 = rco : 1.079E-01 = res : 0.000E+00 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x : -3.23606797749979E+00 0.00000000000000E+00 y : 0.00000000000000E+00 1.27201964951407E+00 == err : 1.174E-15 = rco : 1.079E-01 = res : 0.000E+00 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x : 1.23606797749979E+00 0.00000000000000E+00 y : -7.86151377757423E-01 -9.95682444457783E-60 == err : 3.476E-16 = rco : 1.998E-01 = res : 4.441E-16 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x : 1.23606797749979E+00 0.00000000000000E+00 y : 7.86151377757423E-01 9.95682444457783E-60 == err : 3.476E-16 = rco : 1.998E-01 = res : 4.441E-16 ==