Hasse Principle

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in and all the , then the equations have solutions in the Rationals . Examples include the set of equations

with , , and Integers, and the set of equations

for rational. The trivial solution is usually not taken into account when deciding if a collection of homogeneous equations satisfies the Hasse principle. The Hasse principle is sometimes called the Local-Global Principle.