Randomized and deterministic algorithms for the dimension of algebraic varieties

被引：15

作者：

Koiran, P ^{[1
]}

机构：

[1] Ecole Normale Super Lyon, Lab Informat Parallelisme, F-69364 Lyon 07, France

来源：

38TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS | 1997年

关键词：

D O I：

10.1109/SFCS.1997.646091

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NP-complete in the Blum-Shub-Smale model of computation over C, that it admits a s(O(1))D-O(n) deterministic algorithm, and that for systems with integer coefficients it is in the Arthur-Merlin class under the Generalized Riemann Hypothesis. The first two results are based on a general derandomization argument.

引用

页码：36 / 45

页数：10

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