function f_{1} is discontinuous/abrupt/sharply changes locally (in output) on/at s_{2} (set), with abruptness of type x_{3} (default: 1)

s_{2} should be a set within some open subset of definition of f_{1}, or a set on which f_{1} is not defined at all. For x_{3}, an argument of n (number) corresponds to a differentiability class of order n to which f_{1} does NOT belong at points in set s_{2}; notice that such an n makes no implications about the truth value of f_{1} belonging to any given differentiability classes of order m_{2} will have n ≤ 1. For now at least, n can be a nonnegative integer; generalizations may eventually be defined. This lujvo is not perfectly algorithmic/predictable.