read NearestNpoly;

f1 := 92*x^3+44*x^2*y+40*x*y^2-67*y^3+8*x^2+66*x*y+68*y^2-95*x-62*y-18: 
f2 := 68*x^3+39*x^2*y+20*x*y^2+45*y^3-65*x^2-67*x*y+93*y^2+43*x+8*y+6: 
f := expand(f1*f2)/99;

# Now introduce a significant round-off error:
F := evalf(f, 2);

# With such large error, we can not always expect the program to
# work (hence the warning message) though it does work in this example:
NF := NearestNpoly(F, 9);

"Distance F to f is:", Distance(F, f);
"Distance F to NF is:", Distance(F, NF);
# Again, given the input F, we found a reducible polynomial NF that's
# closer to F than f is.   That NF is reducible is confirmed by the
# monodromy computation (the monodromy is not transitive), or can also
# be confirmed by the TrivialFactoring program:

res := TrivialFactoring(NF, 9);

Digits := 15:
	Distance(expand(res),NF):
	"Distance NF to res is:", evalf(%,6);
Digits := 10: