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An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's...
Trie structures are a convenient way of indexing files in which keys are specified by values of attributes. Records correspond to leaves in the trie. Retrieval proceeds by following a path from the root to a leaf, the choice of edges being determined by attribute values. The size of a trie for a file depends on the order in which attributes are tested. We show that determining minimal size tries is...
Suppose we are given a polynomial in (X1,..., Xr) in r ≥ 1 variables, let m bound the degree of p in all variables Xi, 1≤i≤r, and we wish to raise P to the nth power, n≫1. In a recent paper which compared the iterative versus the binary method it was shown that their respective computing times were O(m2rnr+1) versus O((mn) 2r) when using single precision arithmetic. In this paper a new algorithm is...
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