```2
x1+x2**3;
x1**2*x2-x2**4;

TITLE : decker2, with three regular root and one quadruple root at (0,0)

For the quadruple root at the origin, three deflations are needed.
Moreover, instead of the default tolerance of 1.0E-6 to decide the
numerical rank, 1.0E-4 should be taken, as the initial roots in the
list below are all quite far from (0,0).

REFERENCES:

D.W. Decker, H.B. Keller, C.T. Kelley:
"Convergence rates for Newton's method at singular points."
SIAM J. Numer. Anal. 20, 296-314, 1983

THE SOLUTIONS :
7 2
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 :  1.73208017041855E-06   4.52248120137621E-05
x1 :  6.29486767127907E-15   5.45721660425622E-14
== err :  1.565E-05 = rco :  4.109E-13 = res :  4.185E-14 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 : -5.00000000000000E-01  -8.66025403784439E-01
x1 : -1.00000000000000E+00   8.62816615085482E-32
== err :  4.062E-16 = rco :  9.010E-02 = res :  5.863E-16 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 :  1.00000000000000E+00   0.00000000000000E+00
x1 : -1.00000000000000E+00   0.00000000000000E+00
== err :  0.000E+00 = rco :  1.098E-01 = res :  0.000E+00 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 : -5.00000000000000E-01   8.66025403784439E-01
x1 : -1.00000000000000E+00  -1.11703936774460E-31
== err :  3.772E-16 = rco :  9.010E-02 = res :  5.863E-16 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 : -3.91577428234014E-05   1.48946510335240E-06
x1 :  3.54258255519533E-14  -4.05820144229233E-15
== err :  1.355E-05 = rco :  2.665E-13 = res :  2.715E-14 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 : -1.77357885498062E-06  -4.67185535052115E-05
x1 : -6.87856850461687E-15  -6.01648175281317E-14
== err :  1.616E-05 = rco :  4.525E-13 = res :  4.610E-14 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x2 :  4.74973933678605E-05  -1.81900694130644E-06
x1 : -6.32194110579452E-14   7.29187155171923E-15
== err :  1.644E-05 = rco :  4.760E-13 = res :  4.848E-14 ==
```