4
15.0*b**4*c*d**2 + 6.0*b**4*c**3 + 21.0*b**4*c**2*d - 144.0*b**2*c
- 8.0*b**2*c**2*e
- 28.0*b**2*c*d*e - 648.0*b**2*d + 36.0*b**2*d**2*e + 9.0*b**4*d**3 - 120.0;
30.0*c**3*b**4*d - 32.0*d*e**2*c - 720.0*d*b**2*c - 24.0*c**3*b**2*e
- 432.0*c**2*b**2 + 576.0*e*c - 576.0*d*e + 16.0*c*b**2*d**2*e
+ 16.0*d**2*e**2 + 16.0*e**2*c**2 + 9.0*c**4*b**4 + 5184.0
+ 39.0*d**2*b**4*c**2 + 18.0*d**3*b**4*c - 432.0*d**2*b**2
+ 24.0*d**3*b**2*e - 16.0*c**2*b**2*d*e - 240.0*c;
216.0*d*b**2*c - 162.0*d**2*b**2 - 81.0*c**2*b**2 + 5184.0 + 1008.0*e*c
- 1008.0*d*e
+ 15.0*c**2*b**2*d*e - 15.0*c**3*b**2*e - 80.0*d*e**2*c + 40.0*d**2*e**2
+ 40.0*e**2*c**2;
261.0 + 4.0*d*b**2*c - 3.0*d**2*b**2 - 4.0*c**2*b**2 + 22.0*e*c - 22.0*d*e;
TITLE : the system of Pierrette Cassou-Nogu`es
ROOT COUNTS :
total degree : 1344
2-homogeneous Bezout bound : 368, with partition {{b},{c,d,e}}
generalized Bezout bound : 312
based on (see T.Y.Li, Tianjun Wang and Xiaoshen Wang)
{b} {b} {b} {b} {c d} {c d} {c d e}
{b} {b} {b} {b} {c d} {c d} {c d e} {c d e}
{b} {b} {e} {c d} {c d} {c d e}
{b} {b} {c d} {c d e}
mixed volume : 24
REFERENCES :
Obtained by electronic mail by Carlo Traverso. See the POSSO test suite.
T.Y. Li, Tianjun Wang, Xiaoshen Wang:
"Random Product Homotopy with Minimal BKK Bound",
in: "The Mathematics of Numerical Analysis" ,
Edited by Renegar, J. and Shub, M. and Smale, S. ,
Lectures in Applied Mathematics vol 32, 1996.
Proceedings of the AMS-SIAM Summer Seminar in Applied Mathematics,
Park City, Utah, July 17-August 11, 1995, Park City, Utah".
NOTE :
The system is deficient w.r.t. face normal (0,0,0,-1), with corresponding
double component of solutions at infinity (b,c,c,e).
The corresponding face system is
-8*b**2*c**2*e - 28*b**2*c*d*e + 36*b**2*d**2*e = 0
16*c**2*e**2 - 32*c*d*e**2 + 16*d**2*e**2 = 0
40*c**2*e**2 - 80*c*d*e**2 + 40*d**2*e**2 = 0
22*c*e - 22*d*e = 0
THE SOLUTIONS :
16 4
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -7.54821372735305E-78 1.47284085072902E+01
c : 5.11897562286027E-01 -2.36672343825525E-79
d : -2.87205751065023E-01 1.32304584187543E-79
e : -3.80894550509321E+01 -1.98024646165642E-77
== err : 3.573E-13 = rco : 1.763E-05 = res : 1.091E-11 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 7.54821372735305E-78 -1.47284085072902E+01
c : 5.11897562286027E-01 -2.36672343825525E-79
d : -2.87205751065023E-01 1.32304584187543E-79
e : -3.80894550509321E+01 -1.98024646165642E-77
== err : 3.573E-13 = rco : 1.763E-05 = res : 1.091E-11 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -6.68640299606734E-03 8.94855573620861E-02
c : 5.62348716108504E+01 7.98084362941689E+01
d : 1.09694720379898E+01 -5.08259658932153E+01
e : -7.52233440839102E-02 -5.99175264541474E-02
== err : 2.650E-13 = rco : 3.639E-07 = res : 1.728E-11 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -6.68640299606762E-03 -8.94855573620861E-02
c : 5.62348716108506E+01 -7.98084362941687E+01
d : 1.09694720379896E+01 5.08259658932153E+01
e : -7.52233440839101E-02 5.99175264541477E-02
== err : 1.771E-13 = rco : 3.639E-07 = res : 1.029E-11 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.68640299606752E-03 8.94855573620863E-02
c : 5.62348716108503E+01 -7.98084362941685E+01
d : 1.09694720379896E+01 5.08259658932152E+01
e : -7.52233440839104E-02 5.99175264541477E-02
== err : 8.458E-14 = rco : 3.639E-07 = res : 9.095E-12 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 6.68640299606761E-03 -8.94855573620862E-02
c : 5.62348716108505E+01 7.98084362941687E+01
d : 1.09694720379896E+01 -5.08259658932153E+01
e : -7.52233440839102E-02 -5.99175264541477E-02
== err : 3.486E-13 = rco : 3.639E-07 = res : 2.301E-11 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -5.38538073236606E-04 1.52598333728220E-03
c : -1.07543281631105E+03 5.30600350408460E+03
d : 2.56422532949456E+02 9.41056507764428E+03
e : -3.08017284129789E-03 7.79451935745435E-05
== err : 3.507E-10 = rco : 4.323E-14 = res : 6.269E-10 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -8.34114996980346E-02 -2.50448888097739E-75
c : 4.02749534214863E+01 -2.91833407813751E-72
d : 5.17567280407121E+01 -3.90879897738419E-72
e : 8.62858019518498E-01 7.18529223783858E-75
== err : 7.684E-13 = rco : 8.909E-08 = res : 3.638E-12 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.38538073236606E-04 -1.52598333728220E-03
c : -1.07543281631105E+03 5.30600350408460E+03
d : 2.56422532949456E+02 9.41056507764428E+03
e : -3.08017284129789E-03 7.79451935745435E-05
== err : 3.507E-10 = rco : 4.323E-14 = res : 6.269E-10 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 8.34114996980346E-02 2.50448888097739E-75
c : 4.02749534214863E+01 -2.91833407813751E-72
d : 5.17567280407121E+01 -3.90879897738419E-72
e : 8.62858019518498E-01 7.18529223783858E-75
== err : 7.684E-13 = rco : 8.909E-08 = res : 3.638E-12 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -4.73975992311414E+01 -1.72623882440134E-70
c : 7.08768865860076E-02 -5.42213206563050E-73
d : 3.41971008721347E-03 -9.43069606216313E-75
e : -1.46865638657142E+02 -6.10126377935950E-70
== err : 4.169E-12 = rco : 9.519E-08 = res : 1.734E-12 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 4.73975992311414E+01 1.72623882440134E-70
c : 7.08768865860076E-02 -5.42213206563050E-73
d : 3.41971008721347E-03 -9.43069606216313E-75
e : -1.46865638657142E+02 -6.10126377935950E-70
== err : 4.169E-12 = rco : 9.519E-08 = res : 1.734E-12 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 5.38538073236603E-04 1.52598333728219E-03
c : -1.07543281631105E+03 -5.30600350408462E+03
d : 2.56422532949454E+02 -9.41056507764432E+03
e : -3.08017284129789E-03 -7.79451935745534E-05
== err : 1.891E-10 = rco : 4.323E-14 = res : 4.973E-10 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -4.33810415852418E-82 1.94275907300796E-03
c : 3.88078816153025E+03 -1.35263989994167E-75
d : 7.35174304802575E+03 -2.58599272171609E-75
e : 8.76917468831414E-03 1.82532392122536E-81
== err : 3.453E-10 = rco : 2.633E-14 = res : 2.328E-10 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : 4.33810415852418E-82 -1.94275907300796E-03
c : 3.88078816153025E+03 -1.35263989994167E-75
d : 7.35174304802575E+03 -2.58599272171609E-75
e : 8.76917468831414E-03 1.82532392122536E-81
== err : 3.453E-10 = rco : 2.633E-14 = res : 2.328E-10 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
b : -5.38538073236603E-04 -1.52598333728219E-03
c : -1.07543281631105E+03 -5.30600350408462E+03
d : 2.56422532949454E+02 -9.41056507764432E+03
e : -3.08017284129789E-03 -7.79451935745534E-05
== err : 1.891E-10 = rco : 4.323E-14 = res : 4.973E-10 ==