Algebraic geometry studies the zeros of polynomials. Computational algebraic geometry [1] uses computational tools, a.k.a, tools and software systems, to solve the polynomials.
There are different tools for computational algebraic geometry, mostly spacialized for a particular typology of problems. We want to focus on the specific use of homotopies [3] to solve algebraic geometry problems. This, will be used as the introduction of a new module into a mathematical programming language (e.g., Julia). The implementation of the module will then be used to solve algebraic geometry problems, evaluated against state-of-the-art tools.
In this project we are going implement a Homotopy Theory module to solve algebraic geometry problems, within the Julia programming language [2].
n.cardozo