8
-e*g - 2*d*h;
9*e + 4*b;
-4*c*h - 2*e*f - 3*d*g;
-7*c + 9*a - 8*f;
-4*d*f - 5*c*g - 6*h - 3*e;
-5*d - 6*c*f - 7*g + 9*b;
9*d + 6*a - 5*b;
9*c - 7*a + 8;
TITLE : small system from constructive Galois theory, called s9_1
ROOT COUNTS :
total degree : 16
2-homogeneous Bezout number : 10
with partition : {e d b c a }{g h f }
mixed volume : 10
REFERENCES :
Raphael Nauheim:
"Systems of Algebraic Equations with Bad Reduction",
Universitaet Heidelberg, Interdisziplinaeres Zentrum
fuer wissenschaftliches Rechnen, Preprint 95-46, Dezember 1995.
There are four real and six complex conjugated solutions.
THE SOLUTIONS :
10 8
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : 1.51053285357998E+00 1.80139017713210E+00
g : 2.33683608531618E+00 1.53846965064388E-01
d : -3.21601607265565E+00 5.81267061547841E-01
h : 3.68839339468626E-01 7.57261884400351E-01
b : -3.39869892055495E+00 -4.05312789854722E+00
c : 6.60269451071902E-01 -3.30517224679012E+00
f : 1.66301111489823E+00 -1.88866985530864E+00
a : 1.99177500852102E+00 -4.24950717444445E+00
== err : 6.233E-15 = rco : 1.184E-02 = res : 1.899E-14 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : -6.87611772125171E-01 -1.06910588403688E-50
g : 2.02970578781795E+00 1.87093529706454E-50
d : 6.61372486000091E-01 1.33638235504610E-50
h : 1.05511615859238E+00 5.34552942018439E-51
b : 1.54712648728164E+00 1.87093529706454E-50
c : -6.57722954873121E-01 -2.67276471009220E-51
f : 9.09872597215360E-01 -2.33866912133067E-51
a : 2.97213343734559E-01 -4.00914706513829E-51
== err : 4.818E-15 = rco : 2.538E-02 = res : 1.776E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : 1.51053285357998E+00 -1.80139017713210E+00
g : 2.33683608531618E+00 -1.53846965064389E-01
d : -3.21601607265565E+00 -5.81267061547840E-01
h : 3.68839339468626E-01 -7.57261884400351E-01
b : -3.39869892055495E+00 4.05312789854722E+00
c : 6.60269451071902E-01 3.30517224679012E+00
f : 1.66301111489823E+00 1.88866985530864E+00
a : 1.99177500852102E+00 4.24950717444445E+00
== err : 5.760E-15 = rco : 1.184E-02 = res : 1.432E-14 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : 1.16422080143523E-01 -1.92195753383132E-01
g : 2.63662396247879E-01 5.56482066322579E-02
d : 1.57730288928362E-01 6.27553637263924E-01
h : 2.53243613191786E-02 3.93434985858779E-02
b : -2.61949680322927E-01 4.32440445112047E-01
c : -1.24268975951462E+00 -4.51860436457511E-01
f : 5.75605851705934E-01 -2.58205963690006E-01
a : -4.54886833661648E-01 -5.80963418302514E-01
== err : 4.814E-15 = rco : 3.274E-03 = res : 9.037E-16 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : -1.91397791595386E-01 -3.73380916671669E-60
g : 2.37577797622942E-02 -1.28349690105886E-60
d : 1.14629961437537E+00 1.24460305557223E-59
h : 1.98341974588837E-03 -4.66726145839586E-61
b : 4.30645031089619E-01 8.71222138900560E-60
c : -1.94711665958355E+00 -8.71222138900560E-60
f : 1.73076194523685E-01 -3.42265840282363E-60
a : -1.36057856232171E+00 -1.12014275001501E-59
== err : 1.950E-15 = rco : 2.785E-03 = res : 3.553E-15 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : -4.15425076903867E-01 -7.96941863871104E-01
g : 1.49599564821986E+00 1.08183777510683E+00
d : -4.34678314642327E-01 3.77392003632451E-01
h : 1.09268365680768E+00 -9.39664948170555E-01
b : 9.34706423033702E-01 1.79311919370998E+00
c : 2.24064048678632E-01 7.21916213907501E-01
f : 1.41375088495922E+00 4.12523550804286E-01
a : 1.43093949115824E+00 9.28177989309645E-01
== err : 4.605E-15 = rco : 2.242E-02 = res : 1.986E-15 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : -4.15425076903867E-01 7.96941863871104E-01
g : 1.49599564821986E+00 -1.08183777510683E+00
d : -4.34678314642327E-01 -3.77392003632451E-01
h : 1.09268365680768E+00 9.39664948170555E-01
b : 9.34706423033702E-01 -1.79311919370998E+00
c : 2.24064048678632E-01 -7.21916213907501E-01
f : 1.41375088495922E+00 -4.12523550804286E-01
a : 1.43093949115824E+00 -9.28177989309644E-01
== err : 5.569E-15 = rco : 2.242E-02 = res : 2.512E-15 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : 2.19606992938435E-01 -5.09789411562385E-56
g : 1.05762750111393E-01 5.60768352718623E-56
d : -1.80601046493377E-01 2.44698917549945E-55
h : 6.43026160917456E-02 2.80384176359312E-56
b : -4.94115734111479E-01 1.22349458774972E-55
c : -9.98447866015167E-01 -2.14111552856202E-55
f : 7.15172647991333E-01 -1.12153670543725E-55
a : -1.40861542019500E-01 -2.85482070474935E-55
== err : 5.974E-16 = rco : 2.837E-03 = res : 8.882E-16 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : -2.66666666666667E+00 2.45980994751297E-60
g : 1.71423733988431E-17 -2.60728974609933E-58
d : 1.71423733988431E-17 -2.94321567845557E-60
h : 1.33333333333333E+00 6.56554882968095E-58
b : 6.00000000000000E+00 -5.53457238190418E-60
c : 3.00000000000000E+00 -7.96545955566226E-59
f : 3.00000000000000E+00 7.96545955566226E-59
a : 5.00000000000000E+00 -1.97320133903454E-61
== err : 3.536E-15 = rco : 1.716E-02 = res : 2.057E-16 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e : 1.16422080143523E-01 1.92195753383132E-01
g : 2.63662396247879E-01 -5.56482066322579E-02
d : 1.57730288928362E-01 -6.27553637263924E-01
h : 2.53243613191786E-02 -3.93434985858779E-02
b : -2.61949680322927E-01 -4.32440445112047E-01
c : -1.24268975951462E+00 4.51860436457511E-01
f : 5.75605851705934E-01 2.58205963690006E-01
a : -4.54886833661648E-01 5.80963418302514E-01
== err : 4.767E-15 = rco : 3.274E-03 = res : 1.831E-15 ==