The first application is to determine whether a given real number x is likely to be algebraic, by searching for an integer relation between a set of powers of x {1, x, x2, ..., xn}.
A typical approach in experimental mathematics is to use numerical methods and arbitrary precision arithmetic to find an approximate value for an infinite series, infinite product or an integral to a high degree of precision (usually at least 100 significant figures), and then use an integer relation algorithm to search for an integer relation between this value and a set of mathematical constants.
The higher the precision to which the inputs to the algorithm are known, the greater the level of confidence that any integer relation that is found is not just a numerical artifact.
A notable success of this approach was the use of the PSLQ algorithm to find the integer relation that led to the Bailey–Borwein–Plouffe formula for the value of π. PSLQ has also helped find new identities involving multiple zeta functions and their appearance in quantum field theory; and in identifying bifurcation points of the logistic map.
[14][15] Integer relation algorithms are combined with tables of high precision mathematical constants and heuristic search methods in applications such as the Inverse Symbolic Calculator or Plouffe's Inverter.