```3
x1+x3*x1**3+x1*x3*x2**2-x1*x3;
10*x2-2*x2*x3*x1**2-x3*x2**3-x2*x3;
-6*x3**2*x1**4-3*x1**2*x2**2*x3**2-x3**2*x1**2+28*x3*x1**2
-3*x3**2*x2**4+2*x3**2*x2**2+7*x3*x2**2+x3**2-11*x3+10;

TITLE : ojika4, six triple roots need same double deflation

While there are six triple roots (18 when counted with
multiplicity), deflating twice with the same system suffices
for all of the roots.

REFERENCES :

T. Ojika: "A numerical method for branch points of a system
of nonlinear algebraic equations."
Applied Numerical Mathematics 4, 419--430, 1988.

THE SOLUTIONS :
18 3
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  9.88519842409067E-08  -1.96022379385648E-07
x3 :  9.99999999999956E-01  -5.96238334284083E-14
x2 :  1.76477073888175E-67  -4.98424576498622E-68
== err :  2.059E-07 = rco :  3.398E-14 = res :  8.890E-13 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  7.39554838854006E-07  -1.51000245590543E-06
x3 :  5.50000000001014E+00   1.30692049847827E-11
x2 : -9.04534033732797E-01   6.36850677565126E-13
== err :  1.213E-06 = rco :  1.264E-12 = res :  6.856E-11 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.23587367738388E-76   4.74739420438940E-76
x3 :  9.99999999998018E+00   2.56560706343765E-11
x2 : -1.32956873284468E-06   6.58642181505783E-07
== err :  1.420E-06 = rco :  1.508E-11 = res :  4.238E-10 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.76781486875480E-06   1.39411799850658E-07
x3 :  5.49999999998183E+00   2.88426722929854E-12
x2 :  9.04534033734176E-01  -1.40547764115234E-13
== err :  1.028E-06 = rco :  1.147E-12 = res :  6.220E-11 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.68168685354472E-07   6.93027789179549E-07
x3 :  5.50000000000153E+00  -3.80216218683919E-12
x2 : -9.04534033733216E-01  -1.85275964970148E-13
== err :  6.251E-07 = rco :  2.900E-13 = res :  1.569E-11 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  3.73029195629038E-07  -7.70458607723508E-07
x3 :  5.50000000000266E+00   3.36351421982717E-12
x2 :  9.04534033733161E-01  -1.63901041603303E-13
== err :  6.166E-07 = rco :  3.280E-13 = res :  1.779E-11 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.40309240280482E-07   7.99156366376784E-08
x3 :  1.00000000000044E+00  -1.29525974268576E-13
x2 : -2.39614717334407E-64   4.10052739958494E-65
== err :  4.361E-07 = rco :  1.867E-13 = res :  4.959E-12 ==
solution 8 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.66025403783435E-01  -9.37249588609680E-13
x3 :  4.00000000000927E+00  -8.65794083656534E-12
x2 :  1.96698002993925E-06  -7.75733051376856E-07
== err :  1.479E-06 = rco :  1.145E-12 = res :  5.043E-11 ==
solution 9 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.70412510786665E-07   6.95414686070690E-07
x3 :  5.50000000000154E+00  -3.83373519457606E-12
x2 :  9.04534033733216E-01   1.86814489417025E-13
== err :  6.275E-07 = rco :  2.921E-13 = res :  1.579E-11 ==
solution 10 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.66025403784165E-01   1.23226748720873E-12
x3 :  4.00000000000252E+00   1.13831994472783E-11
x2 : -1.58099479183237E-06  -1.26889862109655E-06
== err :  1.537E-06 = rco :  1.053E-12 = res :  3.916E-11 ==
solution 11 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.08714012970267E-06   1.66572418202861E-07
x3 :  5.49999999997467E+00   4.06870149007878E-12
x2 : -9.04534033734525E-01   1.98264186994621E-13
== err :  1.215E-06 = rco :  1.601E-12 = res :  8.681E-11 ==
solution 12 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.66025403789258E-01  -1.46119709459201E-12
x3 :  3.99999999995548E+00  -1.34979605739893E-11
x2 : -5.93881783406918E-07   4.00556755714356E-06
== err :  2.480E-06 = rco :  4.201E-12 = res :  1.633E-10 ==
solution 13 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  8.66025403783563E-01   8.19156692389163E-13
x3 :  4.00000000000809E+00  -7.56704538979463E-12
x2 :  1.83778076054619E-06  -7.25648656887914E-07
== err :  1.382E-06 = rco :  1.000E-12 = res :  4.406E-11 ==
solution 14 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  2.58571014229383E-07  -6.46631194712484E-07
x3 :  9.99999999999472E-01  -5.08359465894322E-13
x2 :  1.36320744450064E-63   1.58249571212928E-63
== err :  6.369E-07 = rco :  3.437E-13 = res :  9.184E-12 ==
solution 15 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  8.66025403784294E-01  -6.67014862677038E-13
x3 :  4.00000000000134E+00   6.16161936832714E-12
x2 : -1.16058813729580E-06  -9.35635096654522E-07
== err :  1.130E-06 = rco :  5.694E-13 = res :  2.110E-11 ==
solution 16 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  4.78379641388737E-76   3.01110474533727E-76
x3 :  1.00000000000024E+01   3.55226697722828E-12
x2 :  9.10146809095399E-08  -1.12206169433971E-06
== err :  1.122E-06 = rco :  4.282E-12 = res :  3.392E-10 ==
solution 17 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x1 :  8.66025403789250E-01   1.46288806106773E-12
x3 :  3.99999999995555E+00  -1.35135810531887E-11
x2 : -5.95018480832858E-07   4.00253405004135E-06
== err :  2.479E-06 = rco :  4.195E-12 = res :  1.631E-10 ==
solution 18 :
t :  9.99999990123350E-01   0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.42072873892243E-38  -2.87847959467424E-37
x3 :  9.99999999984417E+00  -1.44440240046841E-10
x2 :  3.42446822269255E-06   1.31264664195213E-06
== err :  3.248E-06 = rco :  7.621E-11 = res :  2.426E-09 ==
```