*Quick Intro:* Myself Mahraib Fatima, a third-year Computer Science undergraduate and self-paced Machine Learning student, with interest about algebraic geometry and complex analysis.
*Previous Knowledge:* I have studied complex analysis, algebraic geometry, and Jacobian varieties, which align with the mathematical foundations required for this project. *Project Research:* Since February, I explored SageMath's project list and focused on "*Poincaré Normal Form of Riemann matrices.*" I thoroughly read and analyzed the research paper on Poincaré's Complete Reducibility Theorem, abelian integrals, Riemann surfaces, and topological graphs. *Learning:* I learnt about Riemann matrices, theta functions, and their reducibility, as described in the paper. *Implementation Goal:* The project aims to implement Poincaré's theorem in SageMath, focusing on decomposing Riemann matrices and reducing associated theta functions(As mentioned in project description). *Ambiguity: *The main challenge lies in translating the paper's theoretical algorithms into efficient code, *especially handling edge cases and ensuring numerical stability *(mentor guidance required). *Approach:* I plan to break the implementation into modular steps: Riemann matrix decomposition, theta function reduction, and testing. *Tools:* I will use Python, SageMath, and libraries like NumPy and SymPy for computations and symbolic mathematics. *Outcome:* The project will provide a computational tool for researchers and students, along with documentation and examples. *Motivation:* This project combines my interests in mathematics and programming, allowing me to contribute to the SageMath community while deepening my knowledge. Regards, Mahraib Fatima -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-gsoc+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-gsoc/a3c7bc02-8933-4c2a-88d3-5098d122ba74n%40googlegroups.com.
