An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1 x_1 + a_2 x_2 + ... + a_n x_n = 0, with not all a_i = 0. Although the algorithm operates by manipulating a lattice, it does not reduce it to a short vector basis, and is therefore not a lattice reduction algorithm. PSLQ is based on a partial sum of squares scheme (like the PSOS algorithm) implemented using QR decomposition. It was developed by Ferguson and Bailey. A much simplified version of the algorithm was subsequently developed by Ferguson et al. (1999), which also extends the algorithm to complex numbers and quaternions. Ferguson et al. (1999) also demonstrated that PSLQ is distinct from the HJLS algorithm.

Ferguson-Forcade algorithm | integer relation | LLL algorithm | PSOS algorithm