var x;
var y;

subject to

cons1:  x^2 + 4*y^2 - 4 = 0;
cons2:         2*y^2 - x = 0;

solve;
display x, y;

# 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 ==