Helaman R. P. Ferguson

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Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let x = (x 1 ,. .. , x n) be a vector in K n. The vector x has an integer relation if there exists a vector m = (m 1 ,. .. , m n) ∈ O(K) n , m = 0, such that m 1 x 1 + m 2 x 2 +. .. + m n x n = 0. In this paper we define the parameterized integer(More)
Let x = (x 1 , x 2 , · · · , x n) be a vector of real numbers. x is said to possess an integer relation if there exist integers a i not all zero such that a 1 x 1 + a 2 x 2 + · · · + a n x n = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a i given x. The most efficient of these existing integer relation(More)
Let x = (x 1 ; x 2 ; ; x n) be a vector of real numbers. x is said to possess an integer relation if there exist integers a i not all zero such that a 1 x 1 + a 2 x 2 + + a n x n = 0. Beginning ten years ago, algorithms were discovered by one of us which, for any n, are guaranteed to either nd a relation if one exists or else establish bounds within which(More)
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