6
45*y + 35*u - 165*v - 36;
35*y + 25*z + 40*t - 27*u;
25*y*u - 165*v**2 + 15*x - 18*z + 30*t;
15*y*z + 20*t*u - 9*x;
-11*v**3 + x*y + 2*z*t;
-11*u*v + 3*v**2 + 99*x;
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 ==