6 -10*x1*x6^2+ 2*x2*x6^2-x3*x6^2+x4*x6^2+ 3*x5*x6^2+x1*x6+ 2*x2*x6+x3*x6+ 2*x4* x6+x5*x6+ 10*x1+ 2*x2-x3+ 2*x4-2*x5; 2*x1*x6^2-11*x2*x6^2+ 2*x3*x6^2-2*x4*x6^2+x5*x6^2+ 2*x1*x6+x2*x6+ 2*x3*x6+x4* x6+ 3*x5*x6+ 2*x1+ 9*x2+ 3*x3-x4-2*x5; -x1*x6^2+ 2*x2*x6^2-12*x3*x6^2-x4*x6^2+x5*x6^2+x1*x6+ 2*x2*x6-2*x4*x6-2*x5*x6- x1+ 3*x2+ 10*x3+ 2*x4-x5; x1*x6^2-2*x2*x6^2-x3*x6^2-10*x4*x6^2+ 2*x5*x6^2+ 2*x1*x6+x2*x6-2*x3*x6+ 2*x4* x6+ 3*x5*x6+ 2*x1-x2+ 2*x3+ 12*x4+x5; 3*x1*x6^2+x2*x6^2+x3*x6^2+ 2*x4*x6^2-11*x5*x6^2+x1*x6+ 3*x2*x6-2*x3*x6+ 3*x4* x6+ 3*x5*x6-2*x1-2*x2-x3+x4+ 10*x5; x1+x2+x3+x4+x5-1; TITLE : generalized eigenvalue problem ROOT COUNTS : total degree : 243 2-homogeneous Bezout bound : 10 REFERENCES : M. Chu, T.-Y. Li and T. Sauer; "Homotopy method for general lambda-matrix problems", SIAM J. Matrix Anal. Appl., vol. 9, No. 4, pp 528-536, 1988. THE SOLUTIONS : 10 6 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -4.03104921027674E-01 3.11150763893057E-61 x6 : -5.26884338028681E-01 -2.65611437989453E-61 x2 : 1.02852436023601E+00 -3.11150763893057E-61 x3 : -7.65802783270593E-01 3.11150763893057E-61 x4 : 5.84438864730263E-01 -2.43755812565216E-61 x5 : 5.55944479331990E-01 -6.22301527786114E-61 == err : 3.909E-15 = rco : 7.658E-03 = res : 2.442E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 2.99075932021782E-01 5.01143383142287E-52 x6 : 2.02323961940148E+00 6.68191177523049E-52 x2 : 1.29632560155695E-01 1.00228676628457E-51 x3 : -2.50229425780516E-02 0.00000000000000E+00 x4 : 2.82858256715490E-01 -1.00228676628457E-51 x5 : 3.13456193685084E-01 2.08809742975953E-53 == err : 3.645E-16 = rco : 1.423E-02 = res : 3.553E-15 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 3.61434411929062E-01 5.22024357439882E-54 x6 : -7.93299819295134E-01 1.04404871487976E-53 x2 : 8.62739540151744E-02 3.91518268079912E-54 x3 : 2.30573068453758E-01 0.00000000000000E+00 x4 : -1.78344810664138E-01 -2.61012178719941E-53 x5 : 5.00063376266144E-01 3.39315832335923E-53 == err : 5.305E-16 = rco : 6.558E-02 = res : 6.661E-16 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 3.74914846627566E-01 3.18618382226491E-56 x6 : -9.89067571030006E-01 4.46065735117087E-57 x2 : 2.69467709194748E-01 -8.92131470234173E-57 x3 : 2.01358039843421E-01 -2.16660499914014E-56 x4 : 3.43365652466371E-01 -2.54894705781192E-57 x5 : -1.89106248132106E-01 1.27447352890596E-57 == err : 3.742E-16 = rco : 3.143E-02 = res : 1.443E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.09012520270965E+00 4.17619485951906E-53 x6 : 8.91088225418399E-01 6.78631664671847E-53 x2 : -4.68830940953671E-01 9.18762869094192E-52 x3 : 1.77918152799782E+00 -1.41990625223648E-51 x4 : 1.92190665861778E+00 -2.83981250447296E-51 x5 : -1.14213204295227E+00 3.34095588761524E-51 == err : 5.578E-15 = rco : 1.751E-03 = res : 7.994E-15 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.54640578834680E+00 2.50571691571143E-52 x6 : 4.94356140660691E-01 2.08809742975953E-52 x2 : -2.08005601877580E+00 -1.67047794380762E-52 x3 : 1.78182343900084E+00 -1.25285845785572E-52 x4 : -1.01638636925152E+00 -5.95107767481466E-52 x5 : 7.68213160679684E-01 5.01143383142287E-52 == err : 4.010E-15 = rco : 1.636E-03 = res : 3.553E-15 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 2.49229454860982E-01 2.50571691571143E-52 x6 : 1.45857046356428E+00 -4.17619485951906E-51 x2 : 6.72438547403408E-01 4.00914706513829E-51 x3 : 4.93329668745933E-01 4.67733824266134E-51 x4 : -3.93783458451863E-01 -7.01600736399201E-51 x5 : -2.12142125584604E-02 -6.68191177523049E-52 == err : 8.420E-16 = rco : 1.887E-02 = res : 2.609E-15 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -2.74700924324691E+00 6.57424425150851E-53 x6 : -1.06999188030235E+00 1.03997039958726E-54 x2 : 1.75605089702930E+00 -4.36991483591276E-53 x3 : 3.04134725910012E+00 -6.37032848688356E-53 x4 : -8.33686740566606E-01 3.33606190926425E-53 x5 : -2.16702172315900E-01 7.06568124425465E-54 == err : 5.602E-15 = rco : 1.049E-03 = res : 1.243E-14 == solution 9 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -4.27092363584264E-01 -6.01646293746430E-65 x6 : -1.20380998147538E+00 4.55787251796470E-64 x2 : -1.15167375381329E+00 -4.30958759171515E-63 x3 : 4.93213679643402E-01 -1.13946812949118E-64 x4 : 1.44398220254774E+00 1.40534402637245E-63 x5 : 6.41570235206413E-01 2.94362600118554E-63 == err : 4.029E-15 = rco : 4.001E-03 = res : 7.327E-15 == solution 10 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.43647743849955E+00 -8.81188686806509E-63 x6 : 9.51877558035348E-01 8.96597771651903E-64 x2 : 3.53621608158665E-01 1.35216884699620E-62 x3 : 6.93350523095517E-01 -1.64083410646729E-62 x4 : -3.06921446296540E-01 -3.76784128151749E-62 x5 : 1.69642675354191E+00 4.86173068582902E-62 == err : 1.796E-15 = rco : 2.877E-03 = res : 3.109E-15 ==