```2
x**2;
y**2;

TITLE: first toy example eg1 only needs one deflation

The origin is a root of multiplicity four.
One deflation suffices.

THE SOLUTIONS :
4 2
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x :  3.78374112838220E-09   1.76619586214763E-09
y : -1.21699683285829E-09   3.99437892594574E-09
== err :  1.076E-08 = rco :  9.695E-01 = res :  4.876E-17 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x :  3.78374112838220E-09   1.76619586214763E-09
y :  1.21699683285829E-09  -3.99437892594574E-09
== err :  1.076E-08 = rco :  9.695E-01 = res :  4.876E-17 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x : -3.78374112838220E-09  -1.76619586214763E-09
y : -1.21699683285829E-09   3.99437892594574E-09
== err :  1.076E-08 = rco :  9.695E-01 = res :  4.876E-17 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x : -3.78374112838220E-09  -1.76619586214763E-09
y :  1.21699683285829E-09  -3.99437892594574E-09
== err :  1.076E-08 = rco :  9.695E-01 = res :  4.876E-17 ==
```