I am trying to find a vector field whose value is zero when evaluated at a point (x, y) and x or y is not an integer. That is to say:
$F(x,y) = 0$ if $(x\space or\space y) \notin \mathbb{Z}$
The context is as follows, I am evaluating a line integral, and I want the work done by force on the particle to be zero, if either of the two components of the point on which the particle is located is not an integer.
Anyone know the equation of a field with these properties?
Thanks in advance, I hope I have made myself understood