Abstract

In this paper, we propose some heuristic probabilistic polynomial time algorithms with one-sided error for recognition of cubic hypersurfaces the singular loci of which do not contain any linear subspace of sufficiently large dimension. These algorithms are easy to implement in computer algebra systems. The algorithms are based on checking the condition that the Hessian determinant of a cubic form does not vanish identically or does not determine any cone in the projective space. In turn, the properties of the Hessian can be verified with one-sided-error probabilistic algorithms based on the Schwartz–Zippel lemma.

中文翻译：

---

某些立方超曲面识别的启发式算法

摘要

在本文中，我们提出了一种具有单侧误差的启发式概率多项式时间算法，用于识别立方超曲面，其奇异位点不包含任何足够大尺寸的线性子空间。这些算法易于在计算机代数系统中实现。该算法基于检查三次形的Hessian行列式不能完全消失或不能确定投影空间中任何圆锥的条件。反过来，可以使用基于Schwartz-Zippel引理的单边错误概率算法来验证Hessian的属性。