4 200*x1^3-200*x1*x2+x1-1; -100*x1^2+ 1.10100000000000E+02*x2+ 9.90000000000000E+00*x4-20; 180*x3^3-180*x3*x4+x3-1; -90*x3^2+ 9.90000000000000E+00*x2+ 1.00100000000000E+02*x4-20; TITLE : system derived from optimizing the Wood function ROOT COUNTS : total degree : 36 3-homogeneous Bezout bound : 25 with partition : {x1 }{x2 x4 }{x3 } mixed volume : 9 REFERENCES : J.J. More, B.S. Garbow, K.E. Hillstrom: `Testing unconstrained optimization software.' Trans. Math. Software, Vol 7(1): 17-41, 1981. ( 10(x2-x1^2) ) ( 1-x1 ) G(x)= ( 3sqrt(10)(x4-x3^2) ) ( 1-x3 ) ( sqrt(10)(x2+x4-2) ) ((x2-x4)/sqrt(10) ) H(x):=DG^T(x).G(x) THE SOLUTIONS : 9 4 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.57355835612328E+00 2.84257851022096E-01 x2 : 2.39720627801032E+00 8.95148500287229E-01 x4 : -4.44855937693470E-01 -9.18847124013184E-01 x3 : -5.36397657592245E-01 8.60831364613137E-01 == err : 1.088E-13 = rco : 1.745E-04 = res : 9.484E-14 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -3.12510233943360E-02 2.14850736960187E-66 x2 : 1.65971386855783E-01 0.00000000000000E+00 x4 : 1.84263934696728E-01 -4.15431088876991E-66 x3 : -3.12581710232641E-02 4.74778387287990E-65 == err : 4.342E-16 = rco : 3.022E-01 = res : 2.442E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -9.67974024937616E-01 1.03469743815115E-42 x2 : 9.47139140817886E-01 -2.00167411741164E-42 x4 : 9.51247665792282E-01 2.00247055853101E-42 x3 : -9.69516310331569E-01 -1.03464885797978E-42 == err : 1.716E-13 = rco : 1.054E-04 = res : 1.821E-14 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.57355835612330E+00 -2.84257851022089E-01 x2 : 2.39720627801038E+00 -8.95148500287217E-01 x4 : -4.44855937693522E-01 9.18847124013173E-01 x3 : -5.36397657592227E-01 -8.60831364613156E-01 == err : 5.759E-14 = rco : 1.745E-04 = res : 2.045E-13 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -5.36404369479206E-01 -8.60529486984931E-01 x2 : -4.45172990299157E-01 9.18999078613650E-01 x4 : 2.39751628227483E+00 -8.95297290755507E-01 x3 : 1.57359281312329E+00 -2.84279273572161E-01 == err : 9.315E-14 = rco : 2.029E-04 = res : 1.271E-13 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.00000000000000E+00 -5.10349482937392E-57 x2 : 1.00000000000000E+00 -1.00501696737457E-56 x4 : 1.00000000000000E+00 1.00862631623573E-56 x3 : 1.00000000000000E+00 5.03441935978966E-57 == err : 2.934E-14 = rco : 5.987E-04 = res : 5.684E-14 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.03754146247809E+00 3.63159940802936E-01 x2 : 9.53900262105836E-01 -7.52084316235798E-01 x4 : 9.53161163420767E-01 7.52099393811562E-01 x3 : -1.03680791485365E+00 -3.63506283821887E-01 == err : 1.181E-13 = rco : 8.755E-05 = res : 6.355E-14 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -5.36404369479216E-01 8.60529486984926E-01 x2 : -4.45172990299139E-01 -9.18999078613661E-01 x4 : 2.39751628227481E+00 8.95297290755519E-01 x3 : 1.57359281312328E+00 2.84279273572166E-01 == err : 1.002E-13 = rco : 2.029E-04 = res : 1.608E-13 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.03754146247810E+00 -3.63159940802918E-01 x2 : 9.53900262105873E-01 7.52084316235769E-01 x4 : 9.53161163420728E-01 -7.52099393811532E-01 x3 : -1.03680791485363E+00 3.63506283821881E-01 == err : 1.549E-13 = rco : 8.755E-05 = res : 4.711E-14 ==