 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", "x"2, ..., "x""n"}.The second application is to search for an integer relation between a real number "x" and a set of mathematical constants such as "e", π and ln(2), which will lead to an expression for "x" as a linear combination of these constants.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.