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.
and all the 
, then the equations have solutions in the rationals 
. Examples include the set of equations 
,
, and 
integers, and the set of equations
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.