Homotopy gets real (2024)
This thesis presents the development of a new module for the Julia programming language, designed to decompose the real part of complex curves within the field of computational algebraic geometry. The work leverages homotopic approaches to bridge gaps in existing tools. The core objective is to implement a Julia package inspired by BertiniReal, aiming to efficiently handle the decomposition of algebraic sets into their real components. Julia’s robust features and growing prominence in scientific computing motivate the choice of the language. The thesis details the foundational concepts, the implementation of the new module, and its validation through comparative analysis, demonstrating the reliability and utility.