var t;
var u;
var v;
var x;
var y;
var z;

subject to

cons1:  45*y + 35*u - 165*v - 36 = 0;
cons2:  35*y + 25*z + 40*t - 27*u = 0;
cons3:  25*y*u - 165*v^2 + 15*x - 18*z + 30*t = 0;
cons4:  15*y*z + 20*t*u - 9*x = 0;
cons5:  -11*v^3 + x*y + 2*z*t = 0;
cons6:  -11*u*v + 3*v^2 + 99*x = 0;

solve;
display t, u, v, x, y, z;

# TITLE : system of Trinks from the PoSSo test suite

# ROOT COUNTS :

# total degree : 24
# Bezout bound : 18
#   with set structure :
#     {y u v }
#     {y u z t }
#     {y v z t x }{u v }
#     {y u x }{z t }
#     {y v z }{v t x }{v }
#     {u v x }{v }
# mixed volume : 10

# REFERENCES :

# see the PoSSo test suite.

# THE SOLUTIONS :

# 10 6
# ===========================================================
# solution 1 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y : -8.48565024801726E-01  -1.27713006996600E+00
#  u :  2.90791497560052E-01  -1.20716250315356E+00
#  v : -3.87925598190763E-01  -6.04372974296028E-01
#  z :  4.78484665321442E-01  -1.40654658428524E+00
#  t :  6.39725741728645E-01   1.18174573676988E+00
#  x : -8.70894865902957E-02   1.82955491621577E-02
# == err :  3.969E-15 = rco :  1.353E-03 = res :  3.197E-14 ==
# solution 2 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y :  1.96666666666667E-01  -6.85435790006783E-01
#  u : -7.80000000000000E-01  -9.94987437106620E-01
#  v : -3.30000000000000E-01  -3.97994974842648E-01
#  z : -9.22000000000000E-01  -9.81720937945198E-01
#  t : -1.22333333333333E-01   5.41715382424715E-01
#  x : -1.39000000000000E-02   6.30158710167526E-02
# == err :  7.734E-16 = rco :  9.423E-04 = res :  6.405E-15 ==
# solution 3 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y : -8.48565024801726E-01   1.27713006996600E+00
#  u :  2.90791497560052E-01   1.20716250315356E+00
#  v : -3.87925598190763E-01   6.04372974296028E-01
#  z :  4.78484665321442E-01   1.40654658428524E+00
#  t :  6.39725741728644E-01  -1.18174573676988E+00
#  x : -8.70894865902957E-02  -1.82955491621577E-02
# == err :  3.451E-15 = rco :  1.353E-03 = res :  1.589E-14 ==
# solution 4 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y : -2.94139058814790E-01  -4.81178473189385E-01
#  u : -5.27107740348486E-01   4.94314246398167E-01
#  v : -4.10212294296137E-01  -2.63759555732513E-02
#  z : -5.57139585398522E-01   5.83715843485288E-01
#  t :  2.49786192601790E-01   3.89870878181169E-01
#  x :  2.03956529409314E-02  -2.16413875357711E-02
# == err :  6.168E-16 = rco :  9.228E-04 = res :  7.944E-15 ==
# solution 5 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y :  1.96666666666667E-01   6.85435790006783E-01
#  u : -7.80000000000000E-01   9.94987437106620E-01
#  v : -3.30000000000000E-01   3.97994974842648E-01
#  z : -9.22000000000000E-01   9.81720937945198E-01
#  t : -1.22333333333333E-01  -5.41715382424715E-01
#  x : -1.39000000000000E-02  -6.30158710167526E-02
# == err :  7.734E-16 = rco :  9.423E-04 = res :  6.405E-15 ==
# solution 6 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y :  2.61445164854194E-01  -4.24736468635227E-01
#  u :  3.23321350174264E-01  -6.49660994944693E-01
#  v : -7.82952746997701E-02  -2.53644096434239E-01
#  z :  1.14631468249263E-01  -4.43787851136216E-01
#  t : -8.21672755355810E-02   2.10490645428291E-01
#  x : -1.93581189588659E-02  -4.66393563150483E-03
# == err :  4.571E-16 = rco :  2.991E-04 = res :  5.024E-15 ==
# solution 7 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y : -2.94139058814790E-01   4.81178473189385E-01
#  u : -5.27107740348486E-01  -4.94314246398167E-01
#  v : -4.10212294296137E-01   2.63759555732513E-02
#  z : -5.57139585398522E-01  -5.83715843485288E-01
#  t :  2.49786192601790E-01  -3.89870878181169E-01
#  x :  2.03956529409315E-02   2.16413875357711E-02
# == err :  3.989E-16 = rco :  9.228E-04 = res :  7.324E-15 ==
# solution 8 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y :  2.61445164854194E-01   4.24736468635227E-01
#  u :  3.23321350174264E-01   6.49660994944693E-01
#  v : -7.82952746997701E-02   2.53644096434239E-01
#  z :  1.14631468249263E-01   4.43787851136216E-01
#  t : -8.21672755355810E-02  -2.10490645428291E-01
#  x : -1.93581189588659E-02   4.66393563150483E-03
# == err :  4.571E-16 = rco :  2.991E-04 = res :  5.024E-15 ==
# solution 9 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y : -3.31192652383078E+00   4.69962113784073E-57
#  u : -3.46692707885109E+00   5.57582168896358E-57
#  v : -1.85684328080105E+00   2.48920611114446E-57
#  z : -6.96457243121332E+00   1.38598996268523E-56
#  t :  4.91061769963577E+00  -9.00096929789836E-57
#  x :  6.10801432898409E-01  -1.91171029335894E-57
# == err :  6.824E-15 = rco :  1.197E-03 = res :  5.684E-14 ==
# solution 10 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  y :  2.76457235716270E-01  -5.34125685698989E-66
#  u :  3.55899880880022E-01  -2.37389193643995E-66
#  v : -6.72904761331338E-02  -2.37389193643995E-66
#  z :  4.40994174899312E-02  -6.49185933500251E-67
#  t : -2.92297975889288E-02   4.74778387287990E-66
#  x : -2.79817597349734E-03  -7.41841230137484E-68
# == err :  3.240E-16 = rco :  2.168E-04 = res :  4.441E-16 ==