4

64.632945216*z1**2*z4**2 + 55.661869232*z1**2*z4 - 129.265890432*z1*z2*z3*z4
 - 55.661869232*z1*z2*z3 + 12.201006656*z1*z2*z4 + 48.21149907*z1*z3*z4
 + 50.7965557025*z1*z3 + 71.3989540236*z1*z4**2 + 62.3536335897*z1*z4
 + 64.632945216*z2**2*z3**2 - 12.201006656*z2**2*z3 - 48.21149907*z2*z3**2
 - 71.3989540236*z2*z3*z4 + 9.14136787*z2*z3 + 17.5403018476*z2*z4;

81.3704061375*z1**2*z4**2 + 55.3637563425*z1**2*z4 - 162.740812275*z1*z2*z3*z4
 - 55.3637563425*z1*z2*z3 + 25.032598875*z1*z2*z4 + 21.781944477*z1*z3*z4
 + 24.7967262078*z1*z3 + 55.073652285*z1*z4**2 + 41.688210899*z1*z4
 + 81.3704061375*z2**2*z3**2 - 25.032598875*z2**2*z3 - 21.781944477*z2*z3**2
 - 55.073652285*z2*z3*z4 + 9.56199577*z2*z3 + 20.93013785*z2*z4;

35.2817031945*z1**2*z4**2 + 42.2584220358*z1**2*z4 - 70.563406389*z1*z2*z3*z4
 - 42.2584220358*z1*z2*z3 + 23.8847040258*z1*z2*z4 + 8.0797827915*z1*z3*z4
 + 13.5030253426*z1*z3 + 23.1780987025*z1*z4**2 + 37.033791391*z1*z4
 + 35.2817031945*z2**2*z3**2 - 23.8847040258*z2**2*z3 - 8.0797827915*z2*z3**2
 - 23.1780987025*z2*z3*z4 + 10.3467518726*z2*z3 + 16.946539941*z2*z4;

6.8993630265*z1**2*z4**2 + 43.1035038882*z1**2*z4 - 13.798726053*z1*z2*z3*z4
 - 43.1035038882*z1*z2*z3 + 56.0575143198*z1*z2*z4 + 2.379925759*z1*z3*z4
 + 16.2879242092*z1*z3 + 6.40051015*z1*z4**2 + 42.97692982*z1*z4
 + 6.8993630265*z2**2*z3**2 - 56.0575143198*z2**2*z3 - 2.379925759*z2*z3**2
 - 6.40051015*z2*z3*z4 + 22.5597322388*z2*z3 + 55.41365098*z2*z4;

TITLE : system with a product-decomposition structure

ROOT COUNTS :

total degree : 256
m-homogeneous Bezout number : 96
mixed volume : 26

REFERENCES :

Alexander P. Morgan, Andrew J. Sommese, Charles W. Wampler:
`A product-decomposition theorem for bounding Bezout numbers'
SIAM J. Numer. Anal. 32(4): 1308-1325, 1995.

THE SOLUTIONS :

6 4
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 z1 : -1.01091142205921E-01  -6.84531680564726E-59
 z4 : -4.74122152571664E-02  -9.95682444457783E-59
 z2 :  6.27771477054241E-02   4.26276546533488E-59
 z3 : -1.44165272179869E+00  -2.19050137780712E-58
== err :  1.825E-15 = rco :  1.385E-03 = res :  8.882E-16 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 z1 : -3.03289953393234E-01   6.22301527786114E-61
 z4 : -7.42879674456421E-01   3.36042825004502E-59
 z2 : -2.19563588664023E-01  -6.22301527786114E-61
 z3 :  8.42940459412650E-01  -5.60071375007503E-59
== err :  4.416E-16 = rco :  2.648E-02 = res :  4.108E-15 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 z1 : -1.14783020054975E+00   1.20477575779392E-57
 z4 : -2.97812331674776E-01   5.80604040383833E-58
 z2 :  8.17778764925687E-01   1.49352366668667E-57
 z3 : -1.16651145338396E-01  -1.07035862779212E-58
== err :  3.302E-15 = rco :  1.348E-01 = res :  7.105E-15 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 z1 : -8.04608647260215E-01  -3.67048376324917E-55
 z4 : -6.18580514127412E-01  -3.67048376324917E-55
 z2 : -3.15552092702469E-01  -8.15663058499816E-56
 z3 :  1.70911502744779E-01   3.05873646937431E-56
== err :  6.942E-16 = rco :  2.912E-02 = res :  3.775E-15 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 z1 : -2.93357641309663E-01   2.04192688804819E-61
 z4 : -8.25956886486124E+00   8.55664600705907E-61
 z2 : -1.62789599222105E-01  -1.36128459203212E-61
 z3 :  7.43907364531493E+00  -2.72256918406425E-61
== err :  5.848E-15 = rco :  6.511E-04 = res :  2.274E-13 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 z1 : -8.99679355223739E-02  -9.45898322234894E-58
 z4 :  2.51255419352984E-02   4.18186626672269E-58
 z2 :  6.94221243640974E-01   5.41651249785034E-57
 z3 :  7.82620441959484E-02   1.07533704001441E-57
== err :  9.797E-16 = rco :  6.577E-03 = res :  2.359E-16 ==