3. Applications of the PSLQ Algorithm
There are a number of applications of integer relation detection
algorithms in computational mathematics. One application is to
analyze whether or not a given constant 
, whose value can be
computed to high precision, is algebraic of some degree n or less.
This can be done by first computing the vector 
) to high precision and then applying an
integer relation algorithm to the vector x. If a relation is found,
this integer vector is precisely the set of coefficients of a
polynomial satisfied by 
. Even if a relation is not found,
the resulting bound means that 
cannot possibly be the root of
a polynomial of degree n, with coefficients of size less than the
established bound. Even negative results of this sort are often of
interest.
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