5
 (x1 + x1*x2 + x2*x3 + x3*x4)*x5 - 1;
         (x2 + x1*x3 + x2*x4)*x5 - 2;
                 (x3 + x1*x4)*x5 - 3;
                           x4*x5 - 4;
               x1 + x2 + x3 + x4 + 1;

TITLE : 5-dimensional economics problem

ROOT COUNTS :

total degree : 54
3-homogeneous Bezout number : 20
  with partition : {x1 x2 x3 }{x4 }{x5 }
generalized Bezout number : 16
  based on the set structure :
     {x1 x3 }{x2 x4 }{x5 }
     {x1 x2 }{x3 x4 }{x5 }
     {x1 x3 }{x4 }{x5 }
     {x4 }{x5 }
     {x1 x2 x3 x4 }
mixed volume : 8

REFERENCE :

Alexander Morgan:
`Solving polynomial systems using continuation for engineering
 and scientific problems', Prentice-Hall, Englewood Cliffs, New Jersey, 1987.
(p 148).

NOTE:

Transform the system u = 1/x5 and the total degree equals 8.
See the reduced economics problem, in file redeco5.

THE SOLUTIONS :
8 5
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  7.94799605251120E-01  -1.67047794380762E-51
 x2 : -1.14417041381173E+00  -2.67276471009220E-51
 x3 :  3.05149904685739E-02  -1.00228676628457E-51
 x4 : -6.81144181907962E-01  -1.33638235504610E-51
 x5 : -5.87247180001677E+00   0.00000000000000E+00
== err :  2.614E-16 = rco :  1.940E-02 = res :  2.914E-16 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  8.97399802625561E-01   2.18519562237977E+00
 x2 : -2.46488856119036E+00   1.64476478851049E+00
 x3 : -1.04157021643729E+00  -3.46184909267653E+00
 x4 :  1.60905897500210E+00  -3.68111318213734E-01
 x5 :  2.36228836381592E+00   5.40430833869287E-01
== err :  8.630E-15 = rco :  1.642E-02 = res :  1.115E-14 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -2.50000000000000E-01   0.00000000000000E+00
 x2 : -2.50000000000000E-01  -6.52530446799852E-55
 x3 : -2.50000000000000E-01   0.00000000000000E+00
 x4 : -2.50000000000000E-01   6.83117811493600E-56
 x5 : -1.60000000000000E+01  -4.37195399355904E-54
== err :  1.145E-15 = rco :  9.598E-03 = res :  6.661E-16 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  8.97399802625560E-01  -2.18519562237977E+00
 x2 : -2.46488856119036E+00  -1.64476478851049E+00
 x3 : -1.04157021643729E+00   3.46184909267653E+00
 x4 :  1.60905897500210E+00   3.68111318213733E-01
 x5 :  2.36228836381592E+00  -5.40430833869287E-01
== err :  2.091E-15 = rco :  1.642E-02 = res :  1.381E-14 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -4.47996052511202E-02  -2.24207754291971E-44
 x2 :  1.67977712238073E+00  -2.69049305150365E-43
 x3 : -1.16685956712542E+00   1.79366203433577E-43
 x4 : -1.46811795000419E+00   8.96831017167883E-44
 x5 : -2.72457672763185E+00  -8.96831017167883E-44
== err :  5.140E-16 = rco :  4.078E-02 = res :  9.368E-16 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -1.47399802625560E-01  -2.18519562237977E+00
 x2 : -1.67791479309413E+00   6.38326735148376E-01
 x3 :  2.34742504765713E-01   1.41176117876407E+00
 x4 :  5.90572090953981E-01   1.35107708467322E-01
 x5 :  6.43623590000838E+00  -1.47244527285493E+00
== err :  4.210E-15 = rco :  1.197E-02 = res :  9.919E-15 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -1.47399802625560E-01   2.18519562237977E+00
 x2 : -1.67791479309413E+00  -6.38326735148376E-01
 x3 :  2.34742504765713E-01  -1.41176117876407E+00
 x4 :  5.90572090953981E-01  -1.35107708467322E-01
 x5 :  6.43623590000838E+00   1.47244527285493E+00
== err :  3.883E-15 = rco :  1.197E-02 = res :  5.079E-15 ==
solution 8 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  1.00000000000000E+00   2.13821176807376E-49
 x2 :  1.00000000000000E+00   0.00000000000000E+00
 x3 :  1.00000000000000E+00   3.42113882891801E-49
 x4 : -4.00000000000000E+00  -6.84227765783602E-49
 x5 : -1.00000000000000E+00   2.13821176807376E-49
== err :  6.023E-16 = rco :  6.048E-02 = res :  2.220E-16 ==
