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Explore the second lecture in a series on polyhedral geometry algorithms, covering both theoretical foundations and practical applications. Delve into rational polyhedra, their projections, and conversions between different representation types. Learn about lattice points in rational polyhedra, including existence checking, counting methods, and description techniques with special focus on parametric polyhedra. Understand how quantifier elimination applies to optimizing compilers when working with rational and lattice polyhedra. This 1-hour 22-minute lecture was recorded during the "Francophone Computer Algebra Days" on March 13, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other mathematical talks on CIRM's Audiovisual Mathematics Library (http://library.cirm-math.fr), featuring helpful functionalities like chapter markers, keywords, enriched content with abstracts and bibliographies, and multi-criteria search capabilities.
