```2
x**4;
x-y;

TITLE: toy example eg5 which needs three deflations

The origin occurs with multiplicity four and three deflations
are needed.  Instead of the default tolerance of 1.0E-6, it
is better to use 1.0E-4 to decide the numerical rank.

THE SOLUTIONS :
4 2
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x : -9.13236374920890E-05   2.69781069867375E-04
y : -9.13236374920890E-05   2.69781069867375E-04
== err :  2.407E-04 = rco :  6.413E-11 = res :  8.075E-15 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x : -2.02335802400531E-04  -6.84927281190670E-05
y : -2.02335802400531E-04  -6.84927281190670E-05
== err :  1.806E-04 = rco :  2.705E-11 = res :  2.555E-15 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x :  9.13236374920890E-05  -2.69781069867375E-04
y :  9.13236374920890E-05  -2.69781069867375E-04
== err :  2.407E-04 = rco :  6.413E-11 = res :  8.075E-15 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x :  2.02335802400531E-04   6.84927281190670E-05
y :  2.02335802400531E-04   6.84927281190670E-05
== err :  1.806E-04 = rco :  2.705E-11 = res :  2.555E-15 ==
```