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Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let × = (Xl, • • • , ×n) be a vector in K n. The vector × has an integer relation if there exists a vector m = (ml, . . . , mn) E O(K) n, m =_ O, such that mlx I + m2x 2 +... + mnXn = O. In this paper we define the parameterized integer relation construction algorithm PSLQ(r), wheredoi:10.1090/s0025-5718-99-00995-3 fatcat:2mr2emubxveupovhyqfjp3y2x4