Integer relation algorithm

An integer relation between a set of real numbers x₁, x₂, ..., x_n and a set of integers a₁, a₂, ..., a_n, not all 0, such that

${\displaystyle a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=0.\,}$

An integer relation algorithm is an algorithm for finding integer relations. Specifically, given a set of real numbers known to a given precision, an integer relation algorithm will either find an integer relation between them, or will determine that no integer relation exists with coefficients whose magnitudes are less than a certain upper bound.^[1]