4
( 6.57958984375000E-01-1.87652587890625E-01*i) * (
( 9.37683105468750E-01 -2.88299560546875E-01*i) + 2*(x1+x2+x3+x4) - 8*x1
) * ( x1*x2*x3*x4 - x1*x2 - x2*x3 - x3*x4 - x4*x1 )
- x2*x3*x4 + x2 + x4;
( 6.57958984375000E-01-1.87652587890625E-01*i) * (
( 9.37683105468750E-01 -2.88299560546875E-01*i) + 2*(x1+x2+x3+x4) - 8*x3
) * ( x1*x2*x3*x4 - x1*x2 - x2*x3 - x3*x4 - x4*x1)
- x2*x1*x4 + x2 + x4;
( 6.57958984375000E-01-1.87652587890625E-01*i) * (
( 9.37683105468750E-01 -2.88299560546875E-01*i) + 2*(x1+x2+x3+x4) - 8*x2
) * ( x1*x2*x3*x4 - x1*x2 - x2*x3 - x3*x4 - x4*x1)
- x1*x3*x4 + x1 + x3;
( 6.57958984375000E-01-1.87652587890625E-01*i) * (
( 9.37683105468750E-01 -2.88299560546875E-01*i) + 2*(x1+x2+x3+x4) - 8*x4
) * ( x1*x2*x3*x4 - x1*x2 - x2*x3 - x3*x4 - x4*x1)
- x1*x3*x2 + x1 + x3;
TITLE : the system of E.R. Speer
ROOT COUNTS :
total degree : 625
4-homogeneous Bezout number : 384
generalized Bezout bound based : 246
based on the set structure :
{x1 }{x1 x2 }{x2 x3 }{x3 x4 }{x4 }
{x1 }{x1 x2 }{x2 x3 }{x3 x4 }{x4 }
{x1 }{x1 x2 }{x2 x3 }{x3 x4 }{x4 }
{x1 }{x1 x2 }{x2 x3 }{x3 x4 }{x4 }
but for the exploitation of the symmetry, it is better to use
{x1}{x1 x2}{x2 x3}{x3 x4}{x4}
{x2}{x2 x1}{x1 x4}{x4 x3}{x3}
{x3}{x3 x4}{x4 x1}{x1 x2}{x2}
{x4}{x4 x3}{x3 x2}{x2 x1}{x1}
which yields 271 as bound.
mixed volume : 96
GENERATORS OF SYMMETRY GROUP :
x3 x4 x1 x2
x4 x3 x2 x1
REFERENCES :
Karin Gatermann:
`Symbolic solution of polynomial equation systems with symmetry',
Proceedings of ISSAC-90, pp 112-119, ACM New York, 1990.
NOTE :
Choice of the parameters :
4*beta = ( 6.57958984375000E-01-1.87652587890625E-01*i)i
n = ( 9.37683105468750E-01 -2.88299560546875E-01*i)
The system has 43 regular solutions. Seven paths converged to
highly singular solutions with zero components.
THE SOLUTIONS :
50 4
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.22365256896053E-10 7.47398178725219E-11
x2 : -1.33112429012521E-02 -9.98039204301256E-03
x3 : 2.22365256896070E-10 -7.47398178725209E-11
x4 : 1.33112429012521E-02 9.98039204301256E-03
== err : 1.000E+00 = rco : 5.896E-20 = res : 0.000E+00 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 5.88409928346027E-02 2.41524955507384E-01
x2 : 1.75579783532585E-01 -3.13599845644102E-01
x3 : 5.88409928346027E-02 2.41524955507384E-01
x4 : 1.75579783532585E-01 -3.13599845644102E-01
== err : 4.806E-16 = rco : 3.017E-01 = res : 1.144E-16 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 8.75826273809235E-01 5.45586749459116E-01
x2 : 8.86966368821630E-01 -5.87125931506904E-01
x3 : -8.22575559231062E-01 5.12414777868540E-01
x4 : -7.83936565821678E-01 -5.18925522578564E-01
== err : 1.098E-15 = rco : 5.012E-02 = res : 1.790E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.06479530995021E-01 -1.19866862894240E+00
x2 : 1.25336618459551E+00 1.23041494784966E+00
x3 : 1.76883866889522E+00 9.07275081877902E-01
x4 : 1.25336618459551E+00 1.23041494784966E+00
== err : 4.323E-15 = rco : 1.749E-02 = res : 1.432E-14 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.26943936240198E-01 3.08169578416341E-01
x2 : 6.26943936240198E-01 3.08169578416341E-01
x3 : 6.26943936240198E-01 3.08169578416341E-01
x4 : 6.26943936240198E-01 3.08169578416341E-01
== err : 6.861E-16 = rco : 9.468E-02 = res : 9.930E-16 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.51546756430090E-02 -4.26689081908710E-01
x2 : -7.01366366524981E-02 4.26762893600951E-01
x3 : -7.01366366524981E-02 4.26762893600951E-01
x4 : 4.51546756430090E-02 -4.26689081908710E-01
== err : 2.779E-16 = rco : 1.359E-01 = res : 6.939E-17 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 4.51546756430090E-02 -4.26689081908710E-01
x2 : 4.51546756430089E-02 -4.26689081908710E-01
x3 : -7.01366366524981E-02 4.26762893600951E-01
x4 : -7.01366366524980E-02 4.26762893600951E-01
== err : 4.499E-16 = rco : 1.466E-01 = res : 1.862E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.09398116111961E+00 -1.09107979603420E+00
x2 : 1.06158569315323E+00 9.93192081607197E-01
x3 : 1.06158569315323E+00 9.93192081607196E-01
x4 : 1.09398116111960E+00 -1.09107979603420E+00
== err : 5.661E-15 = rco : 3.437E-02 = res : 8.882E-15 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.26855036536523E+00 -1.34971597178349E+00
x2 : 2.48797736688104E-01 1.11641559795454E+00
x3 : 1.26855036536524E+00 -1.34971597178349E+00
x4 : 1.73914836518560E+00 -1.01522585156644E+00
== err : 9.492E-15 = rco : 1.563E-02 = res : 2.775E-14 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.17775904946614E-11 -5.09506647057000E-11
x2 : 5.43920253549077E-02 4.06428640951655E-02
x3 : 3.17775904946459E-11 5.09506647057087E-11
x4 : -5.43920253549077E-02 -4.06428640951655E-02
== err : 1.000E+00 = rco : 4.091E-21 = res : 0.000E+00 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.22575559231061E-01 5.12414777868539E-01
x2 : 8.86966368821631E-01 -5.87125931506904E-01
x3 : 8.75826273809233E-01 5.45586749459116E-01
x4 : -7.83936565821679E-01 -5.18925522578564E-01
== err : 2.665E-15 = rco : 5.046E-02 = res : 4.783E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.76103601993558E+00 9.14850601763719E-02
x2 : -1.76103601993558E+00 9.14850601763720E-02
x3 : -1.76103601993558E+00 9.14850601763719E-02
x4 : -1.76103601993558E+00 9.14850601763722E-02
== err : 4.678E-15 = rco : 3.265E-01 = res : 2.132E-14 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.51488682232112E-21 3.83129111314145E-20
x2 : -1.87848947990355E+02 -1.06129425619113E+03
x3 : -1.51488685736304E-21 -3.83129111257929E-20
x4 : 1.87848947990355E+02 1.06129425619113E+03
== err : 1.000E+00 = rco : 0.000E+00 = res : 0.000E+00 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.83936565821678E-01 -5.18925522578565E-01
x2 : 8.75826273809233E-01 5.45586749459117E-01
x3 : 8.86966368821631E-01 -5.87125931506903E-01
x4 : -8.22575559231062E-01 5.12414777868540E-01
== err : 1.760E-15 = rco : 5.138E-02 = res : 3.249E-15 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.25778351322786E-01 -2.05525781272223E+00
x2 : 1.08642425044402E-01 1.98318292258550E+00
x3 : 1.25778351322786E-01 -2.05525781272223E+00
x4 : 1.08642425044402E-01 1.98318292258550E+00
== err : 1.737E-14 = rco : 9.262E-03 = res : 2.842E-14 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.09398116111961E+00 -1.09107979603420E+00
x2 : 1.09398116111961E+00 -1.09107979603420E+00
x3 : 1.06158569315323E+00 9.93192081607195E-01
x4 : 1.06158569315323E+00 9.93192081607194E-01
== err : 1.962E-15 = rco : 4.462E-02 = res : 4.172E-15 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 8.86966368821630E-01 -5.87125931506904E-01
x2 : 8.75826273809235E-01 5.45586749459117E-01
x3 : -7.83936565821678E-01 -5.18925522578564E-01
x4 : -8.22575559231062E-01 5.12414777868540E-01
== err : 1.230E-15 = rco : 4.689E-02 = res : 2.701E-15 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.75579783532585E-01 -3.13599845644102E-01
x2 : 5.88409928346027E-02 2.41524955507384E-01
x3 : 1.75579783532585E-01 -3.13599845644102E-01
x4 : 5.88409928346027E-02 2.41524955507384E-01
== err : 4.714E-16 = rco : 2.950E-01 = res : 1.528E-16 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 8.75826273809235E-01 5.45586749459117E-01
x2 : -7.83936565821678E-01 -5.18925522578565E-01
x3 : -8.22575559231062E-01 5.12414777868540E-01
x4 : 8.86966368821631E-01 -5.87125931506905E-01
== err : 1.333E-15 = rco : 5.198E-02 = res : 2.589E-15 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.38347949520814E+00 4.11983223287053E-01
x2 : 2.38347949520814E+00 4.11983223287053E-01
x3 : 2.38347949520814E+00 4.11983223287053E-01
x4 : 2.38347949520813E+00 4.11983223287053E-01
== err : 6.024E-15 = rco : 7.448E-02 = res : 5.905E-14 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.56361653383626E+00 -7.75585851027062E-01
x2 : -9.95572021851750E-01 -1.19749191311902E+00
x3 : -3.85367778330764E-02 1.24595583981227E+00
x4 : -9.95572021851751E-01 -1.19749191311902E+00
== err : 5.237E-15 = rco : 2.147E-02 = res : 1.176E-14 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.47440442167999E-01 1.00747237204140E+00
x2 : -8.14302898360972E-01 -1.05380824958008E+00
x3 : -8.14302898360973E-01 -1.05380824958008E+00
x4 : -8.47440442167999E-01 1.00747237204140E+00
== err : 4.054E-15 = rco : 3.312E-02 = res : 6.061E-15 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.83936565821677E-01 -5.18925522578565E-01
x2 : -8.22575559231062E-01 5.12414777868539E-01
x3 : 8.86966368821631E-01 -5.87125931506903E-01
x4 : 8.75826273809234E-01 5.45586749459116E-01
== err : 8.584E-16 = rco : 5.181E-02 = res : 3.202E-15 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.47440442167999E-01 1.00747237204141E+00
x2 : -8.47440442168000E-01 1.00747237204141E+00
x3 : -8.14302898360975E-01 -1.05380824958007E+00
x4 : -8.14302898360974E-01 -1.05380824958007E+00
== err : 7.304E-15 = rco : 4.137E-02 = res : 9.155E-15 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.06158569315323E+00 9.93192081607199E-01
x2 : 1.06158569315323E+00 9.93192081607196E-01
x3 : 1.09398116111960E+00 -1.09107979603420E+00
x4 : 1.09398116111961E+00 -1.09107979603420E+00
== err : 5.660E-15 = rco : 4.458E-02 = res : 8.882E-15 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.01366366524980E-02 4.26762893600951E-01
x2 : -7.01366366524981E-02 4.26762893600951E-01
x3 : 4.51546756430089E-02 -4.26689081908710E-01
x4 : 4.51546756430090E-02 -4.26689081908710E-01
== err : 4.356E-16 = rco : 1.156E-01 = res : 2.250E-16 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.73914836518560E+00 -1.01522585156644E+00
x2 : 1.26855036536523E+00 -1.34971597178350E+00
x3 : 2.48797736688102E-01 1.11641559795454E+00
x4 : 1.26855036536523E+00 -1.34971597178350E+00
== err : 9.478E-15 = rco : 1.571E-02 = res : 1.638E-14 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 2.48797736688102E-01 1.11641559795454E+00
x2 : 1.26855036536523E+00 -1.34971597178350E+00
x3 : 1.73914836518560E+00 -1.01522585156644E+00
x4 : 1.26855036536523E+00 -1.34971597178350E+00
== err : 2.498E-15 = rco : 1.472E-02 = res : 1.005E-14 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 6.13034422644777E-02 -1.20729648340945E-02
x2 : -8.03488949077827E-12 2.71484765568664E-11
x3 : -6.13034422644777E-02 1.20729648340945E-02
x4 : 8.03488949077517E-12 -2.71484765568654E-11
== err : 1.000E+00 = rco : 1.667E-21 = res : 0.000E+00 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.14302898360974E-01 -1.05380824958008E+00
x2 : -8.14302898360974E-01 -1.05380824958008E+00
x3 : -8.47440442168000E-01 1.00747237204140E+00
x4 : -8.47440442168000E-01 1.00747237204140E+00
== err : 4.327E-15 = rco : 4.077E-02 = res : 4.870E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.14302898360975E-01 -1.05380824958008E+00
x2 : -8.47440442168001E-01 1.00747237204140E+00
x3 : -8.47440442168001E-01 1.00747237204140E+00
x4 : -8.14302898360974E-01 -1.05380824958008E+00
== err : 4.741E-15 = rco : 3.151E-02 = res : 4.731E-15 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.62018357263108E-02 -1.30301652248078E+00
x2 : -1.05750297537461E+00 1.17264315677942E+00
x3 : -1.62350656647767E+00 7.82600700582907E-01
x4 : -1.05750297537461E+00 1.17264315677942E+00
== err : 5.215E-15 = rco : 1.969E-02 = res : 7.324E-15 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.22575559231062E-01 5.12414777868540E-01
x2 : -7.83936565821679E-01 -5.18925522578565E-01
x3 : 8.75826273809234E-01 5.45586749459117E-01
x4 : 8.86966368821631E-01 -5.87125931506904E-01
== err : 5.870E-16 = rco : 5.105E-02 = res : 3.397E-15 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.01366366524981E-02 4.26762893600951E-01
x2 : 4.51546756430089E-02 -4.26689081908710E-01
x3 : 4.51546756430090E-02 -4.26689081908710E-01
x4 : -7.01366366524980E-02 4.26762893600951E-01
== err : 3.129E-16 = rco : 1.357E-01 = res : 2.326E-16 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.37415624992767E-20 6.57192930499547E-22
x2 : 2.46692660367597E+03 4.48192347186842E+01
x3 : 3.37415625380012E-20 -6.57192774083644E-22
x4 : -2.46692660367597E+03 -4.48192347186842E+01
== err : 1.000E+00 = rco : 1.312E-31 = res : 0.000E+00 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.76883866889522E+00 9.07275081877905E-01
x2 : 1.25336618459551E+00 1.23041494784966E+00
x3 : 3.06479530995022E-01 -1.19866862894240E+00
x4 : 1.25336618459551E+00 1.23041494784966E+00
== err : 1.198E-14 = rco : 1.846E-02 = res : 2.543E-14 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -9.95572021851752E-01 -1.19749191311901E+00
x2 : -3.85367778330770E-02 1.24595583981227E+00
x3 : -9.95572021851752E-01 -1.19749191311901E+00
x4 : -1.56361653383626E+00 -7.75585851027062E-01
== err : 6.085E-15 = rco : 1.810E-02 = res : 1.834E-14 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 8.86966368821631E-01 -5.87125931506904E-01
x2 : -8.22575559231062E-01 5.12414777868540E-01
x3 : -7.83936565821678E-01 -5.18925522578565E-01
x4 : 8.75826273809235E-01 5.45586749459117E-01
== err : 5.601E-16 = rco : 7.863E-02 = res : 2.931E-15 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.62350656647767E+00 7.82600700582908E-01
x2 : -1.05750297537461E+00 1.17264315677942E+00
x3 : -5.62018357263107E-02 -1.30301652248078E+00
x4 : -1.05750297537461E+00 1.17264315677942E+00
== err : 7.491E-15 = rco : 2.189E-02 = res : 2.132E-14 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.43379482441545E-03 -2.06769035331036E-03
x2 : -4.29089399313291E-10 -8.73211991328274E-11
x3 : -1.43379482441545E-03 2.06769035331036E-03
x4 : 4.29089399313290E-10 8.73211991328262E-11
== err : 1.000E+00 = rco : 3.772E-19 = res : 0.000E+00 ==
solution 41 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -9.95572021851747E-01 -1.19749191311902E+00
x2 : -1.56361653383626E+00 -7.75585851027063E-01
x3 : -9.95572021851748E-01 -1.19749191311902E+00
x4 : -3.85367778330741E-02 1.24595583981227E+00
== err : 1.934E-15 = rco : 2.025E-02 = res : 1.354E-14 ==
solution 42 :
t : 9.99999838890803E-01 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.10495837961502E-19 -3.53082269351682E-17
x2 : 6.61800495474017E+01 -5.57662781784020E+01
x3 : 4.09142700423076E-19 3.53089242168906E-17
x4 : -6.61800495459465E+01 5.57662781777617E+01
== err : 1.000E+00 = rco : 1.956E-25 = res : 0.000E+00 ==
solution 43 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.25336618459551E+00 1.23041494784966E+00
x2 : 3.06479530995021E-01 -1.19866862894240E+00
x3 : 1.25336618459551E+00 1.23041494784966E+00
x4 : 1.76883866889522E+00 9.07275081877904E-01
== err : 7.276E-15 = rco : 1.795E-02 = res : 1.293E-14 ==
solution 44 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.85367778330728E-02 1.24595583981227E+00
x2 : -9.95572021851747E-01 -1.19749191311902E+00
x3 : -1.56361653383626E+00 -7.75585851027062E-01
x4 : -9.95572021851747E-01 -1.19749191311902E+00
== err : 3.090E-15 = rco : 1.821E-02 = res : 1.432E-14 ==
solution 45 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.26855036536524E+00 -1.34971597178350E+00
x2 : 1.73914836518560E+00 -1.01522585156644E+00
x3 : 1.26855036536524E+00 -1.34971597178350E+00
x4 : 2.48797736688105E-01 1.11641559795454E+00
== err : 8.594E-15 = rco : 1.752E-02 = res : 2.139E-14 ==
solution 46 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.25336618459551E+00 1.23041494784966E+00
x2 : 1.76883866889522E+00 9.07275081877902E-01
x3 : 1.25336618459551E+00 1.23041494784966E+00
x4 : 3.06479530995022E-01 -1.19866862894241E+00
== err : 7.625E-15 = rco : 2.135E-02 = res : 1.855E-14 ==
solution 47 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.05750297537462E+00 1.17264315677942E+00
x2 : -5.62018357263122E-02 -1.30301652248078E+00
x3 : -1.05750297537461E+00 1.17264315677942E+00
x4 : -1.62350656647767E+00 7.82600700582909E-01
== err : 6.416E-15 = rco : 1.993E-02 = res : 1.470E-14 ==
solution 48 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.05750297537462E+00 1.17264315677942E+00
x2 : -1.62350656647767E+00 7.82600700582906E-01
x3 : -1.05750297537461E+00 1.17264315677942E+00
x4 : -5.62018357263111E-02 -1.30301652248078E+00
== err : 5.446E-15 = rco : 2.138E-02 = res : 8.882E-15 ==
solution 49 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.08642425044401E-01 1.98318292258551E+00
x2 : 1.25778351322782E-01 -2.05525781272222E+00
x3 : 1.08642425044399E-01 1.98318292258550E+00
x4 : 1.25778351322784E-01 -2.05525781272222E+00
== err : 4.717E-15 = rco : 9.430E-03 = res : 2.842E-14 ==
solution 50 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.06158569315323E+00 9.93192081607198E-01
x2 : 1.09398116111961E+00 -1.09107979603420E+00
x3 : 1.09398116111961E+00 -1.09107979603420E+00
x4 : 1.06158569315323E+00 9.93192081607195E-01
== err : 5.459E-15 = rco : 3.305E-02 = res : 1.785E-14 ==