5 x1^2-x1+x2+x3+x4+x5-10; x2^2+x1-x2+x3+x4+x5-10; x3^2+x1+x2-x3+x4+x5-10; x4^2+x1+x2+x3-x4+x5-10; x5^2+x1+x2+x3+x4-x5-10; TITLE : system of A.H. Wright ROOT COUNTS : total degree : 32 mixed volume : 32 REFERENCES : M. Kojima and S. Mizuno: `Computation of all solutions to a system of polynomial equations' Math. Programming, vol 25, pp 131-157, 1983. A.H. Wright: `Finding all solutions to a system of polynomial equations' Math. Comp., vol 44, pp 125-133, 1985. W. Zulehner: `A simple homotopy method for determining all isolated solutions to polynomial systems' Math. Comp., vol 50, no 161, pp 167-177, 1988. THE GENERATING SOLUTIONS : 6 5 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 10 the solution for t : x1 : 3.00000000000000E+00 0.00000000000000E+00 x2 : 3.00000000000000E+00 7.59645419660784E-65 x3 : -1.00000000000000E+00 -7.59645419660784E-65 x4 : 3.00000000000000E+00 -6.07716335728627E-64 x5 : -1.00000000000000E+00 0.00000000000000E+00 == err : 2.737E-48 = rco : 3.111E-01 = res : 3.039E-63 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 5 the solution for t : x1 : 2.37228132326901E+00 -1.10542957505209E-74 x2 : 2.37228132326901E+00 -6.63257745031253E-75 x3 : -3.72281323269014E-01 -7.25438158627933E-76 x4 : 2.37228132326901E+00 -3.59264611891929E-75 x5 : 2.37228132326901E+00 2.10031619259897E-74 == err : 4.524E-15 = rco : 3.334E-01 = res : 5.664E-74 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 10 the solution for t : x1 : 4.00000000000000E+00 4.34083096949019E-65 x2 : 4.00000000000000E+00 0.00000000000000E+00 x3 : -2.00000000000000E+00 -7.59645419660784E-65 x4 : -2.00000000000000E+00 -5.90835326402832E-65 x5 : -2.00000000000000E+00 -6.07716335728627E-64 == err : 2.737E-48 = rco : 2.727E-01 = res : 2.947E-63 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 5 the solution for t : x1 : 5.37228132326901E+00 9.33452291679171E-61 x2 : -3.37228132326902E+00 -1.08902767362570E-60 x3 : -3.37228132326901E+00 -1.08902767362570E-60 x4 : -3.37228132326901E+00 -9.33452291679171E-61 x5 : -3.37228132326901E+00 -1.01123998265244E-60 == err : 4.771E-15 = rco : 3.456E-01 = res : 1.776E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 2.00000000000000E+00 5.93472984109987E-67 x2 : 2.00000000000000E+00 -5.93472984109987E-67 x3 : 2.00000000000000E+00 0.00000000000000E+00 x4 : 2.00000000000000E+00 -5.29886592955346E-68 x5 : 2.00000000000000E+00 -5.29886592955346E-68 == err : 2.673E-51 = rco : 2.881E-01 = res : 1.293E-66 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -5.00000000000000E+00 4.06888611498885E-27 x2 : -5.00000000000000E+00 4.06888611498885E-27 x3 : -5.00000000000000E+00 2.13018155431769E-26 x4 : -5.00000000000000E+00 1.93870456067116E-26 x5 : -5.00000000000000E+00 0.00000000000000E+00 == err : 1.371E-09 = rco : 4.667E-01 = res : 2.068E-25 ==