4
 3*x**2-2*x-a;
 x**3-x**2-x*a+a-2*b-2;
 3*y**2-2*y-a;
 y**3-y**2-y*a-a+2;

TITLE : the system of Solotarev from the PoSSo test suite

ROOT COUNTS :

total degree : 36
4-homogeneous Bezout number : 10
  with partition {{x }{a }{b }{y }}
generalized Bezout number : 8
  with the set structure :
    {x a }{x }
    {x b }{x a }{x }
    {a y }{y }
    {a y }{y }{y }
mixed volume : 6

REFERENCES :

See the PoSSo test suite.

THE SOLUTIONS :

6 4
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x : -1.00000016764979E+00   8.30237643136911E-08
 a :  5.00000134119829E+00  -6.64190114509508E-07
 b :  3.00000134119829E+00  -6.64190114509508E-07
 y : -1.00000016764979E+00   8.30237643136911E-08
== err :  1.497E-06 = rco :  1.393E-08 = res :  1.402E-13 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x :  1.66666683444954E+00  -8.29578757360181E-08
 a :  5.00000134226302E+00  -6.63663005888127E-07
 b : -1.74074118816175E+00   2.21221001962709E-07
 y : -1.00000016778288E+00   8.29578757360185E-08
== err :  1.496E-06 = rco :  1.980E-08 = res :  1.400E-13 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x : -3.33333333333333E-01   0.00000000000000E+00
 a :  1.00000000000000E+00   0.00000000000000E+00
 b : -4.07407407407407E-01   0.00000000000000E+00
 y :  1.00000000000000E+00   0.00000000000000E+00
== err :  4.163E-16 = rco :  2.522E-01 = res :  5.551E-17 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x : -9.99999867089384E-01  -1.49761124852549E-07
 a :  4.99999893671507E+00   1.19808899882038E-06
 b :  2.99999893671507E+00   1.19808899882038E-06
 y : -9.99999867089384E-01  -1.49761124852549E-07
== err :  1.602E-06 = rco :  1.570E-08 = res :  1.604E-13 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x :  1.00000000000000E+00   0.00000000000000E+00
 a :  1.00000000000000E+00   0.00000000000000E+00
 b : -1.00000000000000E+00   0.00000000000000E+00
 y :  1.00000000000000E+00   0.00000000000000E+00
== err :  0.000E+00 = rco :  4.667E-01 = res :  0.000E+00 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x :  1.66666653366608E+00   1.49659837765391E-07
 a :  4.99999893599533E+00   1.19727870212311E-06
 b : -1.74074038607252E+00  -3.99092900707705E-07
 y : -9.99999866999416E-01  -1.49659837765391E-07
== err :  1.602E-06 = rco :  2.232E-08 = res :  1.604E-13 ==