```3
x1+x2+x3-1;
0.2*x1**3+0.5*x2**2-x3+0.5*x3**2+0.5;
x1+x2+0.5*x3**2-0.5;

TITLE : ojika3, needs one deflation with different systems

This system has one root of multiplicity four and another
root of multiplicity two.  For both roots, one deflation
suffices, but the deflated systems are different, as the
numerical rank of the Jacobian matrix of the original system
is different for different clusters.

REFERENCES :

T. Ojika, S. Watanabe, and T. Mitsui: "Deflation algorithm
for the multiple roots of a system of nonlinear equations."
J. Math. Anal. Appl. 96, 463-479, 1983.

THE SOLUTIONS :
6 3
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.50000090252499E+00   2.90368755567384E-07
x2 :  2.50000135378748E+00  -4.35553133350855E-07
x3 :  9.99999548737505E-01   1.45184377783471E-07
== err :  3.578E-06 = rco :  1.729E-08 = res :  4.706E-13 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  7.75740356597569E-08  -3.82831846722857E-07
x2 :  5.98217505952537E-08   4.40213430502877E-07
x3 :  9.99999862604214E-01  -5.73815837800202E-08
== err :  1.155E-06 = rco :  3.605E-08 = res :  1.372E-13 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.27729624315320E-07   3.14383400896888E-07
x2 : -2.73579106519331E-08  -3.72418807599902E-07
x3 :  9.99999599628286E-01   5.80354067030143E-08
== err :  1.601E-06 = rco :  6.133E-08 = res :  1.244E-13 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.49999962963196E+00  -1.15854517911605E-07
x2 :  2.49999944444794E+00   1.73781776867394E-07
x3 :  1.00000018518402E+00  -5.79272589557885E-08
== err :  1.452E-06 = rco :  7.047E-09 = res :  7.837E-14 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  1.20590219602005E-07  -6.07683419190186E-07
x2 :  1.60140440371271E-07   4.84080555470448E-07
x3 :  9.99999719269340E-01   1.23602863719738E-07
== err :  1.777E-06 = rco :  6.520E-08 = res :  1.820E-13 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  5.40928071143848E-08   8.10911604128108E-07
x2 :  2.69427735612677E-07  -4.22442959960439E-07
x3 :  9.99999676479457E-01  -3.88468644167669E-07
== err :  2.269E-06 = rco :  9.660E-08 = res :  2.368E-13 ==
```