A force field is described by #<F_x,F_y,F_z> = < xy , 2z-y +x, 2y -z > #. Is this force field conservative?
The definitive evidence of a conservative field
.....then a necessary but insufficient condition is that the curl of the field be zero. (IOW the curl could be zero but the field still be non -conservative, but if the field is conservative the curl has to be zero)
We test that here: