With regards to the termination criteria in step 6, it sometimes
happens that a relation is missed at the point of potential detection
because the y entry is not quite as small as the detection threshold
being used (the threshold is typically set to the ``epsilon'' of the
precision level). When this happens, however, one will note that the
ratio of the smallest and largest y vector entries is suddenly very
small, provided sufficient numeric precision is being used. In a
normal computer run using the PSLQ algorithm, prior to the detection
of a relation, this ratio is seldom smaller than 
. Thus if
this ratio suddenly decreases to a very small value, such as
, then almost certainly a relation has been detected --- one
need only adjust the detection threshold for the algorithm to
terminate properly and output the relation. When detection does
occur, this ratio may be thought of as a ``confidence level'' of the
detection.
Annotation Form Interface