```3
x1**2+x2+x3-1;
x1+x2**2+x3-1;
x1+x2+x3**2-1;

TITLE : ojika2, two regular and three double roots, one deflation

The system has two regular roots and three double roots,
for which one deflation suffices.

REFERENCES :

T. Ojika: "Modified deflation algorithm for the solution of
singular problems. I. A system of nonlinear algebraic equations."
J. Math. Anal. Appl. 123, 199-221, 1987.

THE SOLUTIONS :
8 3
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  2.55401909702350E-07   1.15513090510306E-07
x2 :  2.55401909702350E-07   1.15513090510306E-07
x3 :  9.99999744598090E-01  -1.15513090510306E-07
== err :  1.113E-06 = rco :  4.856E-08 = res :  3.331E-13 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.14213562373095E-01   1.75240110224570E-57
x2 :  4.14213562373095E-01   6.57150413342137E-58
x3 :  4.14213562373095E-01  -2.38963786669868E-57
== err :  4.119E-16 = rco :  6.017E-02 = res :  3.331E-16 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  9.99999713390212E-01  -1.67781352689919E-07
x2 :  2.86609788584706E-07   1.67781352689919E-07
x3 :  2.86609788573014E-07   1.67781352689919E-07
== err :  1.363E-06 = rco :  7.573E-08 = res :  4.508E-13 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.00000002452496E+00  -1.19643680400072E-08
x2 : -2.45249649981224E-08   1.19643680400072E-08
x3 : -2.45249649194714E-08   1.19643680400072E-08
== err :  1.073E-07 = rco :  6.082E-09 = res :  3.093E-15 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.21703146098215E-08   5.43170638278471E-10
x2 :  1.00000001217031E+00  -5.43170638278467E-10
x3 : -1.21703147139869E-08   5.43170638278470E-10
== err :  2.170E-08 = rco :  2.119E-09 = res :  2.249E-16 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.89786129600717E-07   2.57827303828198E-07
x2 :  1.00000018978613E+00  -2.57827303828199E-07
x3 : -1.89786129720831E-07   2.57827303828198E-07
== err :  1.343E-06 = rco :  7.460E-08 = res :  3.847E-13 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.77948078949377E-08  -1.70530076619273E-07
x2 : -8.77948078949377E-08  -1.70530076619273E-07
x3 :  1.00000008779481E+00   1.70530076619274E-07
== err :  7.750E-07 = rco :  3.339E-08 = res :  1.540E-13 ==
solution 8 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.41421356237309E+00  -4.09243983395689E-111
x2 : -2.41421356237309E+00  -3.95902465688893E-111
x3 : -2.41421356237309E+00  -1.58010228437802E-110
== err :  1.507E-14 = rco :  4.142E-01 = res :  6.902E-110 ==
```