var x1;
var x2;
var x3;
var x4;
var x5;
var x6;

subject to

cons1: -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 = 0;
cons2:  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 = 0;
cons3: -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 = 0;
cons4: 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 = 0;
cons5:  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 = 0;
cons6: x1+x2+x3+x4+x5-1 = 0;

solve;
display x1, x2, x3, x4, x5, x6;

# 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 ==