Normal projection: deterministic and probabilistic algorithms |
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| Authors: | Dongmei Li Jinwang Liu Weijun Liu |
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| Affiliation: | 1. Department of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China; 2. Department of Mathematics and Statistics, Central South University, Changsha 410083, China |
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| Abstract: | We consider the following problem: for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature. |
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| Keywords: | Normal projection primary decomposition of ideal deterministic algorithm |
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