Hanan update trap

The Hanan Trap method is a technique that uses inequalities to confine or “trap” values within specific bounds, helping analyze critical points such as prime factors or function behaviors. When applied without poles, it relies solely on smooth inequalities to set these limits. Introducing a pole—a point where the function becomes infinite or undefined—sharpens the trap by creating a singularity that highlights key values more precisely. Thus, the main difference is that the inequality-only approach provides general bounds, while the pole-based method offers tighter, more precise trapping by leveraging singular behavior.