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.
