In the algebraic-geometry-based theory of automated proving and discovery, it is often required that the user includes, as complementary hypotheses, some intuitively obvious non-degeneracy conditions. Traditionally there are two main procedures to introduce such conditions into the hypotheses set. The aim of this paper is to present these two approaches, namely Rabinowitsch’s trick and the ideal saturation computation, and to discuss in detail the close relationships and subtle differences that exist between them, highlighting the advantages and drawbacks of each one. We also present a carefully developed example which illustrates the previous discussion. Moreover, the paper will analyze the impact of each of these two methods in the formulation of statements with negative theses, yielding rather unexpected results if Rabinowitsch’s trick is applied. All the calculations have been carried out using the software Singular in the FinisTerrae 2 supercomputer.

中文翻译：

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处理自动化证明中的负面条件：工具和挑战。拉比诺维奇诡计的意外后果

在基于代数几何的自动证明和发现理论中，通常要求用户包括一些直观明显的非简并条件作为补充假设。传统上有两个主要程序可以将这些条件引入假设集中。本文的目的是介绍这两种方法，即 Rabinowitsch 的技巧和理想的饱和度计算，并详细讨论它们之间存在的密切关系和细微差别，突出每种方法的优缺点。我们还提供了一个精心开发的示例，它说明了前面的讨论。此外，本文将分析这两种方法中的每一种在制定带有否定论文的陈述中的影响，如果应用 Rabinowitsch 的技巧，会产生相当意外的结果。所有计算均使用 FinisTerrae 2 超级计算机中的软件 Singular 进行。