Desingularization Algorithms: A Comparison from the Practical Point of View

TL;DR

This paper reviews various desingularization algorithms, comparing their methods and practical efficiency, and discusses their implementation in the Singular computer algebra system.

Contribution

It provides a comparative overview of different desingularization algorithms and evaluates their practical applicability within Singular.

Findings

Different algorithms vary significantly in efficiency and applicability.

Implementation in Singular enables practical use of multiple desingularization methods.

The overview guides users in selecting suitable algorithms for specific problems.

Abstract

Over the last decade, implementations of several desingularization algorithms have appeared in various contexts. These differ as widely in their methods and in their practical efficiency as they differ in the situations in which they may be applied. The purpose of this article is to give a brief overview over a selection of these approaches and the applicability of the respective implementations in Singular.