Frontiers of Mathematics in China >
Normal projection: deterministic and probabilistic algorithms
Received date: 13 Jul 2013
Accepted date: 04 Dec 2013
Published date: 01 Feb 2014
Copyright
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.
Dongmei LI , Jinwang LIU , Weijun LIU . Normal projection: deterministic and probabilistic algorithms[J]. Frontiers of Mathematics in China, 2014 , 9(1) : 93 -99 . DOI: 10.1007/s11464-013-0349-z
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