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

subject to

cons1: x1^2-x1+x2+x3+x4+x5-10 = 0;
cons2: x2^2+x1-x2+x3+x4+x5-10 = 0;
cons3: x3^2+x1+x2-x3+x4+x5-10 = 0;
cons4: x4^2+x1+x2+x3-x4+x5-10 = 0;
cons5: x5^2+x1+x2+x3+x4-x5-10 = 0;

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

# 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 ==