Editing Newton's method (section)

===Over {{mvar|p}}-adic numbers===
In {{mvar|p}}-adic analysis, the standard method to show a polynomial equation in one variable has a {{mvar|p}}-adic root is [[Hensel's lemma]], which uses the recursion from Newton's method on the {{mvar|p}}-adic numbers. Because of the more stable behavior of addition and multiplication in the {{mvar|p}}-adic numbers compared to the real numbers (specifically, the unit ball in the {{mvar|p}}-adics is a ring), convergence in Hensel's lemma can be guaranteed under much simpler hypotheses than in the classical Newton's method on the real line.