10 5*x1*x2+ 5*x1+ 3*x2+ 55; 7*x2*x3+ 9*x2+ 9*x3+ 19; 3*x3*x4+ 6*x3+ 5*x4-4; 6*x4*x5+ 6*x4+ 7*x5+ 118; x5*x6+ 3*x5+ 9*x6+ 27; 6*x6*x7+ 7*x6+x7+ 72; 9*x7*x8+ 7*x7+x8+ 35; 4*x8*x9+ 4*x8+ 6*x9+ 16; 8*x9*x10+ 4*x9+ 3*x10-51; 3*x1*x10-6*x1+x10+ 5; TITLE : 10-dimensional system of Ku ROOT COUNTS : total degree : 1024 10-homogeneous Bezout number : 2 with partition : {x1 }{x2 }{x3 }{x4 }{x5 }{x6 }{x7 }{x8 }{x9 }{x10 } generalized Bezout number : 2 based on the set structure : {x1 }{x2 } {x2 }{x3 } {x3 }{x4 } {x4 }{x5 } {x5 }{x6 } {x6 }{x7 } {x7 }{x8 } {x8 }{x9 } {x9 }{x10 } {x1 }{x10 } mixed volume : 2 REFERENCES : M.C. Steenkamp : `Die numeriese oplos van stelsels polinoomvergelykings'. Technical report, Nasionale Navorsingsinstituut vir Wiskundige Wetenskappe, Pretoria, 1982. NOTE : This system was known as an easy system for elimination, but difficult for homotopy continuation. With multi-homogenization, this is also an easy system for homotopy continuation methods. THE SOLUTIONS : 2 10 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 2.00000000000000E+00 -2.67276471009220E-51 x2 : -5.00000000000000E+00 -5.34552942018439E-51 x3 : -1.00000000000000E+00 -4.17619485951906E-52 x4 : 5.00000000000000E+00 4.00914706513829E-51 x5 : -4.00000000000000E+00 2.00457353256915E-51 x6 : -3.00000000000000E+00 4.17619485951906E-53 x7 : 3.00000000000000E+00 8.35238971903811E-53 x8 : -2.00000000000000E+00 2.08809742975953E-53 x9 : 4.00000000000000E+00 3.34095588761525E-52 x10 : 1.00000000000000E+00 -1.67047794380762E-52 == err : 3.762E-35 = rco : 6.097E-03 = res : 1.604E-50 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 7.73143904674611E+00 -6.81046792009123E-57 x2 : -2.24828375286041E+00 -9.75768795568627E-58 x3 : -1.83222958057395E-01 -1.11516433779272E-57 x4 : 1.14583333333333E+00 2.34981056892037E-57 x5 : -9.00000000000000E+00 7.16891360009604E-57 x6 : -3.32551987064446E+00 -1.54330778890956E-58 x7 : 2.57062493671946E+00 -1.24460305557223E-58 x8 : -2.19569105036795E+00 -1.19481893334934E-58 x9 : 2.59354917484962E+00 -1.99136488891557E-59 x10 : 1.71067585997878E+00 -9.95682444457783E-59 == err : 4.749E-15 = rco : 3.440E-03 = res : 1.421E-14 ==