4 
 ( 7.67718790000000E-01 + 3.28202780000000E-01*i)*x1*x3
+( 7.67718790000000E-01 + 3.28202780000000E-01*i)*x1*x4
+(-1.76771879000000E+00 - 3.28202780000000E-01*i)*x1
+( 5.48909490000000E-01 + 1.09394900000000E-01*i)*x3
+( 4.79608000000000E-02 + 8.88686780000000E-01*i);
 ( 3.30100210000000E-01 + 8.90584170000000E-01*i)*x2*x3
+( 3.30100210000000E-01 + 8.90584170000000E-01*i)*x2*x4
+(-1.33010021000000E+00 - 8.90584170000000E-01*i)*x2
+( 1.11290920000000E-01 + 6.71774920000000E-01*i)*x4
+( 8.29151510000000E-01 + 6.69877470000000E-01*i);
 (-7.67718790000000E-01 - 3.28202780000000E-01*i)*x1*x3
+(-7.67718790000000E-01 - 3.28202780000000E-01*i)*x1*x4
+(-8.92481630000000E-01 - 4.52965620000000E-01*i)*x3*x4
+( 7.67718790000000E-01 + 3.28202780000000E-01*i)*x1
+(-5.48909490000000E-01 - 1.09394900000000E-01*i)*x3;
 (-3.30100210000000E-01 - 8.90584170000000E-01*i)*x2*x3
+(-3.30100210000000E-01 - 8.90584170000000E-01*i)*x2*x4
+(-8.92481630000000E-01 - 4.52965620000000E-01*i)*x3*x4
+( 3.30100210000000E-01 + 8.90584170000000E-01*i)*x2
+(-1.11290920000000E-01 - 6.71774920000000E-01*i)*x4;

TITLE : lumped-parameter chemically reacting system

ROOT COUNTS :

total degree : 16
4-homogeneous Bezout number : 8
  with partition : {x1 }{x3 }{x4 }{x2 }
generalized Bezout number : 11
  based on the set structure :
     {x1 }{x3 x4 }
     {x3 x4 }{x2 }
     {x1 x4 }{x3 x4 }
     {x3 x2 }{x4 x2 }
mixed volume : 7

REFERENCES :

T.Y. Li and X. Wang:
`Solving deficient polynomial systems with homotopies which keep the
 subschemes at infinity invariant'
Math. Comp., 56(194):693--710, 1991.

THE SOLUTIONS : 

4 4
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -7.31946270990745E-01   3.45282894413807E-01
 x3 :  2.96125742484022E+00   7.79531334186353E+00
 x4 :  5.47960966576759E-02  -9.98459435938367E-02
 x2 :  4.92444390092549E-02   1.26473584413808E-01
== err :  7.155E-14 = rco :  8.372E-04 = res :  9.155E-16 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  8.90824374327220E-01  -8.04191545444130E-01
 x3 :  1.65730911752914E+00  -1.60704603265004E+00
 x4 : -5.65236181483837E-01   5.91969194503908E-01
 x2 :  1.67201508432722E+00  -1.02300085544413E+00
== err :  3.505E-15 = rco :  1.976E-02 = res :  1.256E-15 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -2.21409313579331E+00   1.07437202505838E+00
 x3 :  6.87353439387281E-01  -1.02860646625644E+00
 x4 :  1.66607991847987E+00   7.64394178351801E-01
 x2 : -1.43290242579331E+00   8.55562715058377E-01
== err :  5.643E-15 = rco :  5.514E-02 = res :  1.780E-15 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  4.33734859250612E-02   7.50365995187170E-01
 x3 :  1.02702785627962E-01   2.78773736114270E-01
 x4 :  4.60230559530168E-01  -6.94768664549850E-02
 x2 :  8.24564195925061E-01   5.31556685187170E-01
== err :  4.856E-16 = rco :  6.703E-02 = res :  1.495E-16 ==