3 -9 - t2**2 - t3**2 - 3*t2**2*t3**2 + 8*t2*t3; -9 - t3**2 - t1**2 - 3*t3**2*t1**2 + 8*t3*t1; -9 - t1**2 - t2**2 - 3*t1**2*t2**2 + 8*t1*t2; 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>