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We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere S n , which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.

Polynomial factorization plays a significant role in computational mathematics and its application to engineering, since it forms a fundamental part of algorithms for higher algebraic computations. Multivariate polynomial factorization over finite fields is very important for computations of mathematical object over positive characteristic fields, which… (More)

To give an efficiently computable representation of the zeros of a zero-dimensional ideal I, Rouillier (1996) introduced the rational univariate representation (RUR) as an extension of the generalized shape lemma (GSL) proposed by Alonso et al. (1996). In this paper, we propose a new method to compute the RUR of the radical of I, and report on its practical… (More)

- Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, Yun Guan, Jan Verschelde +14 others
- 2007