var t1;
var t2;
var t3;

subject to

cons1:  -9 - t2^2 - t3^2 - 3*t2^2*t3^2 + 8*t2*t3 = 0;
cons2:  -9 - t3^2 - t1^2 - 3*t3^2*t1^2 + 8*t3*t1 = 0;
cons3:  -9 - t1^2 - t2^2 - 3*t1^2*t2^2 + 8*t1*t2 = 0;

solve;
display t1, t2, t3;

# TITLE : conformal analysis of cyclic molecules, first instance

# ROOT COUNTS :

# total degree : 64
# 3-homogeneous Bezout bound : 16
# mixed volume : 16

# REFERENCES :

# Ioannis Z. Emiris:
# `Sparse Elimination and Application in Kinematics'
# PhD Thesis, Computer Science, University of California at Berkeley, 1994.

# Ioannis Z. Emiris:
# `A general Solver Based on Sparse Resultants:
#  Numerical Issues and Kinematic Applications',
# INRIA Rapport de Recherche no 3110, January 1997, 29 pages
# Available via anonymous ftp to ftp.inria.fr

# THE SOLUTIONS :

# 16 3
# ===========================================================
# solution 1 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  1.16877089448037E+00  -6.05000333706056E-01
#  t3 :  1.16877089448037E+00  -6.05000333706056E-01
#  t1 :  5.35201484207521E-01   1.20233530218111E+00
# == err :  2.569E-15 = rco :  2.564E-01 = res :  1.831E-15 ==
# solution 2 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  1.16877089448037E+00  -6.05000333706056E-01
#  t3 :  5.35201484207521E-01   1.20233530218111E+00
#  t1 :  1.16877089448037E+00  -6.05000333706056E-01
# == err :  2.702E-15 = rco :  2.157E-01 = res :  2.979E-15 ==
# solution 3 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  1.16877089448037E+00   6.05000333706056E-01
#  t3 :  1.16877089448037E+00   6.05000333706056E-01
#  t1 :  5.35201484207521E-01  -1.20233530218111E+00
# == err :  2.569E-15 = rco :  2.564E-01 = res :  1.831E-15 ==
# solution 4 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  5.35201484207521E-01   1.20233530218111E+00
#  t3 :  1.16877089448037E+00  -6.05000333706056E-01
#  t1 :  1.16877089448037E+00  -6.05000333706056E-01
# == err :  2.786E-15 = rco :  2.494E-01 = res :  3.878E-15 ==
# solution 5 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  1.16877089448037E+00   6.05000333706056E-01
#  t3 :  1.16877089448037E+00   6.05000333706056E-01
#  t1 :  1.16877089448037E+00   6.05000333706056E-01
# == err :  2.569E-15 = rco :  4.545E-01 = res :  1.831E-15 ==
# solution 6 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  5.35201484207521E-01  -1.20233530218111E+00
#  t3 :  1.16877089448037E+00   6.05000333706056E-01
#  t1 :  1.16877089448037E+00   6.05000333706056E-01
# == err :  2.569E-15 = rco :  2.494E-01 = res :  3.202E-15 ==
# solution 7 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  1.16877089448037E+00   6.05000333706056E-01
#  t3 :  5.35201484207521E-01  -1.20233530218111E+00
#  t1 :  1.16877089448037E+00   6.05000333706056E-01
# == err :  2.688E-15 = rco :  2.157E-01 = res :  2.220E-15 ==
# solution 8 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 :  1.16877089448037E+00  -6.05000333706056E-01
#  t3 :  1.16877089448037E+00  -6.05000333706056E-01
#  t1 :  1.16877089448037E+00  -6.05000333706056E-01
# == err :  2.569E-15 = rco :  4.545E-01 = res :  1.831E-15 ==
# solution 9 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -5.35201484207521E-01  -1.20233530218111E+00
#  t3 : -1.16877089448037E+00   6.05000333706056E-01
#  t1 : -1.16877089448037E+00   6.05000333706056E-01
# == err :  2.816E-15 = rco :  2.157E-01 = res :  5.515E-15 ==
# solution 10 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -1.16877089448037E+00   6.05000333706056E-01
#  t3 : -1.16877089448037E+00   6.05000333706056E-01
#  t1 : -5.35201484207521E-01  -1.20233530218111E+00
# == err :  2.569E-15 = rco :  2.564E-01 = res :  1.831E-15 ==
# solution 11 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -1.16877089448037E+00  -6.05000333706056E-01
#  t3 : -5.35201484207521E-01   1.20233530218111E+00
#  t1 : -1.16877089448037E+00  -6.05000333706056E-01
# == err :  2.702E-15 = rco :  2.157E-01 = res :  2.979E-15 ==
# solution 12 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -1.16877089448037E+00   6.05000333706056E-01
#  t3 : -5.35201484207521E-01  -1.20233530218111E+00
#  t1 : -1.16877089448037E+00   6.05000333706056E-01
# == err :  2.683E-15 = rco :  2.032E-01 = res :  2.442E-15 ==
# solution 13 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -1.16877089448037E+00   6.05000333706056E-01
#  t3 : -1.16877089448037E+00   6.05000333706056E-01
#  t1 : -1.16877089448037E+00   6.05000333706056E-01
# == err :  2.569E-15 = rco :  4.545E-01 = res :  1.831E-15 ==
# solution 14 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -5.35201484207521E-01   1.20233530218111E+00
#  t3 : -1.16877089448037E+00  -6.05000333706056E-01
#  t1 : -1.16877089448037E+00  -6.05000333706056E-01
# == err :  2.569E-15 = rco :  2.494E-01 = res :  3.202E-15 ==
# solution 15 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -1.16877089448037E+00  -6.05000333706056E-01
#  t3 : -1.16877089448037E+00  -6.05000333706056E-01
#  t1 : -5.35201484207521E-01   1.20233530218111E+00
# == err :  2.569E-15 = rco :  2.564E-01 = res :  1.831E-15 ==
# solution 16 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  t2 : -1.16877089448037E+00  -6.05000333706056E-01
#  t3 : -1.16877089448037E+00  -6.05000333706056E-01
#  t1 : -1.16877089448037E+00  -6.05000333706056E-01
# == err :  2.569E-15 = rco :  4.545E-01 = res :  1.831E-15 ==
# <\PRE>
# <\HTML>