Editing Hasse principle (section)

==Intuition==
Given a polynomial equation with rational coefficients, if it has a rational solution, then this also yields a real solution and a ''p''-adic solution, as the rationals embed in the reals and ''p''-adics: a global solution yields local solutions at each prime. The Hasse principle asks when the reverse can be done, or rather, asks what the obstruction is: when can you patch together solutions over the reals and ''p''-adics to yield a solution over the rationals: when can local solutions be joined to form a global solution?

One can ask this for other [[ring (algebra)|rings]] or [[field (algebra)|fields]]: integers, for instance, or [[number field]]s. For number fields, rather than reals and ''p''-adics, one uses complex embeddings and <math>\mathfrak p</math>-adics, for [[prime ideal]]s <math>\mathfrak p</math>.