3
5.38354663405080E+08*x2^6+ 5.03135199444000E+08*x2^5+
8.95258362000000E+07*x2^4-6.25000000000000E+13*x1^2*x3+
5.77586040000000E+06*x2^3+ 107358*x2^2+ 617*x2+ 1;
-5.03135199444000E+08*x2^5-1.79051672400000E+08*x2^4+ 6.25000000000000E+13
*x1^2*x2+ 1.87500000000000E+14*x1^2*x3-1.73275812000000E+07*x2^3+ 20250000
*x1*x2-429432*x2^2-3085*x2-6;
-5.55555555555555E+15*x1^2+ 1.11111111111111E+16*x1*x3+ 1800000000*x2+ 1;
TITLE : problem 601, coming from electrochemistry
ROOT COUNTS :
total degree : 60
3-homogeneous Bezout number : 48
with partition : {x2 }{x1 }{x3 }
generalized Bezout number : 34
based on the set structure :
{x2 x1 }{x2 x1 }{x2 x3 }{x2 }{x2 }{x2 }
{x2 x3 }{x2 x1 }{x2 x1 }{x2 }{x2 }
{x2 x1 }{x1 x3 }
mixed volume : 18
REFERENCES :
L.T. Watson.
`Globally convergent homotopy methods: a tutorial.
Appl. Math. Comput., 31(Spec. Issue):369--396, 1989.
NOTE :
The scaled system has 18 finite solutions.
De-scaling back to the original coordinates makes that 3 solutions
fail to be approximates for the true solutions of the system.
---------------------------------------------------------------------
| TIMING INFORMATION SUMMARY on juno, Wed 5 Nov 1997 |
---------------------------------------------------------------------
| root counts | start system | continuation | total time |
---------------------------------------------------------------------
| 0h 0m 0s 34ms | 0h 0m 0s787ms | 0h 0m20s178ms | 0h 0m21s325ms |
---------------------------------------------------------------------
THE SOLUTIONS :
15 3
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -7.25805372901499E-01 1.40013566433530E-82
x1 : 1.13267128276082E-03 -4.02152936677190E-85
x3 : 6.70143755976064E-04 -3.61937643009471E-86
== err : 3.208E-16 = rco : 6.335E-06 = res : 1.749E-08 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.48030297185225E-05 4.12311836490762E-05
x1 : -1.58621604838585E-05 2.72212652443695E-05
x3 : -8.17846686445923E-06 1.36071825802625E-05
== err : 4.404E-20 = rco : 3.038E-08 = res : 6.804E-10 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.48030297185225E-05 -4.12311836490762E-05
x1 : -1.58621604838585E-05 -2.72212652443695E-05
x3 : -8.17846686445923E-06 -1.36071825802625E-05
== err : 4.404E-20 = rco : 3.038E-08 = res : 6.804E-10 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.79753388607537E-03 3.02700442741163E-04
x1 : -6.11915910154367E-07 1.47229329556451E-06
x3 : -1.37798440237789E-04 -2.49938473158384E-04
== err : 3.616E-18 = rco : 1.955E-11 = res : 9.313E-10 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -1.69467450435956E-02 -1.06169892227416E-03
x1 : -3.33252787010258E-08 -2.55931624735299E-06
x3 : -8.11742600306796E-05 1.07036125782306E-03
== err : 3.543E-17 = rco : 3.645E-11 = res : 4.657E-10 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.12134388423491E-02 -3.29126160686788E-02
x1 : -1.56461412462451E-05 3.58863386679536E-06
x3 : -8.30790906178326E-04 -5.27740340761898E-04
== err : 7.127E-17 = rco : 1.390E-09 = res : 3.072E-08 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -4.92207628089561E-03 2.67589656948029E-59
x1 : -1.47535767566305E-06 1.99786745370786E-62
x3 : -5.41200700556775E-04 -2.80035687503751E-60
== err : 1.013E-17 = rco : 1.082E-11 = res : 8.882E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -7.24468371562951E-01 -5.39760534693403E-79
x1 : -1.12504448363903E-03 1.26506375318766E-80
x3 : -6.66841562353025E-04 -2.10843958864610E-81
== err : 1.907E-16 = rco : 6.314E-06 = res : 1.192E-06 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -1.69467450435956E-02 1.06169892227416E-03
x1 : -3.33252787010257E-08 2.55931624735299E-06
x3 : -8.11742600306795E-05 -1.07036125782306E-03
== err : 3.519E-17 = rco : 3.645E-11 = res : 4.657E-10 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.28516277142569E-02 -3.39881530129233E-02
x1 : 1.60131916619861E-05 -4.09845171837016E-06
x3 : 8.07010140554413E-04 5.46296064967121E-04
== err : 7.255E-17 = rco : 1.571E-09 = res : 1.490E-08 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -6.34684428050862E-03 9.11574503592941E-64
x1 : 1.12082450749626E-06 -5.37834891849676E-67
x3 : 9.17910699087859E-04 4.93769522779510E-64
== err : 4.115E-18 = rco : 9.918E-12 = res : 1.863E-09 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.12134388423491E-02 3.29126160686789E-02
x1 : -1.56461412462451E-05 -3.58863386679537E-06
x3 : -8.30790906178325E-04 5.27740340761898E-04
== err : 1.804E-16 = rco : 1.390E-09 = res : 2.980E-08 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -2.79753388607537E-03 -3.02700442741163E-04
x1 : -6.11915910154366E-07 -1.47229329556450E-06
x3 : -1.37798440237790E-04 2.49938473158385E-04
== err : 3.337E-18 = rco : 1.955E-11 = res : 3.492E-10 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : -9.28516277142569E-02 3.39881530129233E-02
x1 : 1.60131916619861E-05 4.09845171837016E-06
x3 : 8.07010140554413E-04 -5.46296064967121E-04
== err : 7.255E-17 = rco : 1.571E-09 = res : 1.490E-08 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x2 : 4.66889844311746E-05 3.88938454866321E-62
x1 : 3.22097501038582E-05 3.03858167864314E-63
x3 : 1.58700484713607E-05 5.16558885369333E-63
== err : 4.455E-20 = rco : 3.535E-08 = res : 7.276E-11 ==