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In this paper we consider deterministic computation of the exact determinant of a dense matrix M of integers. We present a new algorithm with worst case complexity O ? n 4 (log n + log jjMjj) + n 3 log 2 jjMjj , where n is the dimension of the matrix and jjMjj is a bound on the entries in M, but with average expected complexity O ? n 4 + n 3 (log n + log(More)
We address the problem of computing ideals of polynomials which vanish at a finite set of points. In particular we develop a modular Buchberger–Möller algorithm, best suited for the computation over Q, and study its complexity; then we describe a variant for the computation of ideals of projective points, which uses a direct approach and a new stopping(More)
Let X be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal I(X) independent of the data uncertainty. We present a method to compute a polynomial basis B of I(X) which exhibits structural stability, that is, if e X is any set of points differing only slightly from X, there exists a(More)
We gather together several bounds on the sizes of coefficients which can appear in factors of polynomials in Z[x]; we include a new bound which was latent in a paper by Mignotte, and a few minor improvements to some existing bounds. We compare these bounds and show that none is universally better than the others. In the second part of the paper we give(More)
The Force Concept Inventory (FCI) has influenced the development of many research-based pedagogies. However, no data exists on the FCI's internal consistency or test-retest reliability. The FCI was administered twice to one hundred students during the first week of classes in an electricity and magnetism course with no review of mechanics between test(More)
Several methods for demonstrating antibody to Crimean-Congo haemorrhagic fever virus were compared on serum samples taken from 101 patients during the acute stage of illness and at intervals for up to 59 months thereafter, with emphasis on early detection of the immune response. The deaths of 23 patients on days 5-14 of illness were ascribed to the effects(More)